September 24, 2025

Citigroup Global Markets Inc.

Morgan Stanley & Co. LLC

As Representatives of the several Underwriters

c/o Citigroup Global Markets Inc.

388 Greenwich Street

New York, NY 10013

c/o Morgan Stanley & Co. LLC

1585 Broadway

New York, New York 10036

Ladies and Gentlemen:

Transocean Ltd., a company organized under the laws of Switzerland (the “Company”), proposes to issue and sell to the several underwriters named in Schedule I hereto (the “Underwriters”), on the terms set forth in this Underwriting Agreement (this “Agreement”), 125,000,000 shares, par value $0.10 per share (the “Firm Shares”) and, at the election of the Underwriters, up to 18,750,000 additional shares, par value $0.10 per share (the “Additional Shares,” together with the Firm Shares, the “Shares”). The shares of the Company are generally referred to as the “Company Shares.” Citigroup Global Markets Inc. and Morgan Stanley & Co. LLC have agreed to act as the representatives of the several Underwriters (each a “Representative” and together, the “Representatives”) in connection with the offering and sale of the Company Shares.

The Company has filed with the Securities and Exchange Commission (the “Commission”) an automatic shelf registration statement on Form S-3 (File No. 333- 280617), including a prospectus (the “Basic Prospectus”), relating to the securities, including the Shares, to be issued from time to time by the Company. The term “Registration Statement” means such registration statement, as of its most recent effective date, including the information (if any) deemed to be part of the registration statement at the time of effectiveness pursuant to Rule 430A or Rule 430B under the Securities Act of 1933, as amended (the “Securities Act”), on the date of such registration statement’s effectiveness for purposes of Section 11 of the Securities Act, as such section applies to the Company and the Underwriters for the Shares pursuant to Rule 430B(f)(2) under the Securities Act (the “Effective Date”).

For purposes of this Agreement, “free writing prospectus” has the meaning set forth in Rule 405 under the Securities Act, “Preliminary Prospectus” means the Basic Prospectus, as amended and supplemented by a preliminary prospectus supplement dated

September 24, 2025 relating to the Shares immediately prior to the Time of Sale (as defined herein), “Time of Sale Prospectus” means the Preliminary Prospectus, together with the documents and pricing information set forth in Schedule II hereto, and “broadly available road show” means a “bona fide electronic road show” as defined in Rule 433(h)(5) under the Securities Act. “Prospectus” means the Basic Prospectus together with the Time of Sale Prospectus, as first filed with the Commission pursuant to Rule 424 under the Securities Act. “Time of Sale” means 7:00 p.m. (New York Time) on the date of this Agreement. As used herein, the terms “Registration Statement,” ”Basic Prospectus,” “Preliminary Prospectus,” “Time of Sale Prospectus” and “Prospectus” shall include the documents, if any, incorporated by reference therein as of the date hereof. The terms “supplement,” “amendment” and “amend” as used herein with respect to the Registration Statement, the Basic Prospectus, the Time of Sale Prospectus or the Prospectus shall include all documents subsequently filed by the Company with the Commission pursuant to the Securities Exchange Act of 1934, as amended (the “Exchange Act”), that are deemed to be incorporated by reference therein (the “Incorporated Documents”).

1.Representations and Warranties. The Company represents and warrants to and agrees with the Underwriters that:

(a)The Registration Statement has become effective; no stop order suspending the effectiveness of the Registration Statement is in effect; and no proceedings for such purpose or pursuant to Section 8A under the Securities Act are pending before or threatened by the Commission.

(b)Each document, if any, filed or to be filed pursuant to the Exchange Act and incorporated by reference in the Time of Sale Prospectus or the Prospectus complied or will comply when so filed in all material respects with the Exchange Act and the applicable rules and regulations of the Commission thereunder, the Registration Statement, when it became effective, did not contain and, will not, as amended or supplemented, contain any untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein not misleading, the Registration Statement, the Preliminary Prospectus and the Prospectus comply and, as amended or supplemented, if applicable, will comply in all material respects with the Securities Act and the applicable rules and regulations of the Commission thereunder, and (i) the Time of Sale Prospectus does not, as of the Time of Sale, (ii) the Prospectus and any amendment or supplement thereto will not, as of their dates, and (iii) the Prospectus, as it may be amended or supplemented pursuant to Section 5 hereof, as of the Closing Date (as defined herein), and any Option Closing Date (as defined herein), as applicable, will not, and (iv) each broadly available road show, if any, when considered together with the Time of Sale Prospectus, does not,contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements therein, in the light of the circumstances under which they were made, not misleading, except that the

representations and warranties set forth in this paragraph do not apply to (A) statements or omissions in the Registration Statement, the Preliminary Prospectus or the Prospectus based upon information relating to the Underwriters furnished to the Company in writing by the Underwriters expressly for use therein, it being understood and agreed that the only such information furnished by the Underwriters consists of the information described as such in paragraph 8(b) below and (B) any Form T-1 Statement of Eligibility and Qualification included as an exhibit to the Registration Statement.

(c)At the determination date for purposes of the offering of the Shares within the meaning of Rule 164(h) under the Securities Act, the Company was not an “ineligible issuer” as used in Rule 164, Rule 405, and Rule 433 under the Securities Act.

(d)Any free writing prospectus that the Company is required to file pursuant to Rule 433(d) under the Securities Act has been, or will be, filed with the Commission in accordance with the requirements of the Securities Act and the applicable rules and regulations of the Commission thereunder. Each free writing prospectus that the Company has filed, or is required to file, pursuant to Rule 433(d) under the Securities Act or that was prepared by or on behalf of or used or referred to by the Company complies or will comply in all material respects with the requirements of the Securities Act and the applicable rules and regulations of the Commission thereunder. Except for the free writing prospectuses, if any, identified in Schedule II hereto, and electronic road shows, if any, each furnished to and approved by the Underwriters before first use, the Company has not prepared, used or referred to, and will not, without the Underwriters’ prior consent, prepare, use or refer to, any free writing prospectus.

(e)The Company has been duly incorporated and is validly existing as a corporation under the laws of Switzerland, with power and authority (corporate and other) to own its properties and conduct its business as described in the Registration Statement, the Time of Sale Prospectus and the Prospectus, and has been duly qualified as a foreign corporation for the transaction of business and is in good standing under the laws of each other jurisdiction in which it owns or leases properties or conducts any business so as to require such qualification, except where the failure to be so qualified would not have a Material Adverse Effect (as defined below); and each Significant Subsidiary (as set forth in Rule 1-02 of Regulation S-X under the Exchange Act) of the Company has been duly incorporated and is validly existing and in good standing (if applicable) under the laws of its jurisdiction of organization, each with power and authority (corporate and other) to own its properties and conduct its business as described in the Registration Statement, the Time of Sale Prospectus and the Prospectus, and each has been duly qualified as a foreign corporation for the transaction of business and is in good standing (if applicable) under the laws of each other jurisdiction in which it owns or leases properties or conducts any business so as to require such

qualification, except where the failure to be so qualified or the failure to have the requisite power and authority would not have a Material Adverse Effect.

(f)This Agreement has been duly authorized, executed and delivered by the Company.

(g)The execution, delivery and performance by the Company, and compliance by the Company with all of the provisions of this Agreement and the consummation of the transactions herein contemplated will not (i) conflict with or result in a breach or violation of any of the terms or provisions of, or constitute a default under, any indenture, mortgage, deed of trust, loan agreement or other agreement or instrument to which the Company or any of the Company’s subsidiaries (the “Subsidiaries”) is a party or by which the Company or any of the Subsidiaries is bound or to which any of the property or assets of the Company or any of the Subsidiaries is subject, nor will any such actions result in any violation of any order, rule or regulation of any court or governmental agency or body having jurisdiction over the Company or any of the Subsidiaries or any of their properties, except for any such conflict, breach, violation or default which (A) would not have a material adverse effect on the general affairs, management, financial position, shareholders’ equity, results of operations, condition (financial or otherwise), prospects, earnings, business or properties of the Company and the Subsidiaries considered as one enterprise (a “Material Adverse Effect”), (B) would not impair the Company’s ability to perform its obligations hereunder or under the Registration Statement, the Time of Sale Prospectus and the Prospectus, as the case may be, and (C) would not have any material adverse effect upon the consummation of the transactions contemplated hereby and thereby, (ii) result in any violation of or default under the provisions of the Articles of Association, Certificate of Incorporation or Bylaws, Organizational Regulations or equivalent document, as the case may be, of the Company or any of the Subsidiaries or (iii) contravene any federal, state or local law, rule or regulation applicable to the Company or any of the Subsidiaries, or any order applicable to the Company or any of the Subsidiaries of any court or of any other governmental agency or instrumentality having jurisdiction over them or any of their property, except for any contravention which (A) would not have a Material Adverse Effect, (B) would not impair the Company’s ability to perform its obligations hereunder or under the Registration Statement, the Time of Sale Prospectus and the Prospectus and (C) would not have any material adverse effect upon the consummation of the transactions contemplated hereby and thereby. The Company will conduct the offer and sale of the Shares in compliance with Rule 415(a)(4) under the Exchange Act.

(h)None of the Company or any of the Subsidiaries has sustained since the date of the latest audited financial statements included or incorporated by reference in the Time of Sale Prospectus, any material loss or interference with its business from fire, explosion, flood or other calamity, whether or not covered

by insurance, or from any labor dispute or court or governmental action, order or decree, otherwise than as set forth in the Time of Sale Prospectus, except for losses or interferences that would not, individually or in the aggregate, have a Material Adverse Effect; and, since the respective dates as of which the information is given in the Time of Sale Prospectus, there has not been any change in the Company Shares (other than pursuant to any employee benefit plan of the Company or issuances of Company Shares to any of the Subsidiaries as treasury shares) or increase in the long-term debt of the Company or any of the Subsidiaries or any incurrence of material liabilities or obligations, direct or contingent, or entry into any material transaction or any change that would have a Material Adverse Effect or any development involving a prospective change that the Company would reasonably expect to have a Material Adverse Effect, otherwise than as set forth or contemplated in the Time of Sale Prospectus.

(i)The statements set forth in the Prospectus under the caption “Description of Transocean Ltd. Shares,” insofar as they purport to constitute a summary of the terms of the Shares, and under the caption “Material Tax Consequences,” insofar as they purport to describe the provisions of the laws referred to therein, are accurate, complete and fair in all material respects.

(j)The Company has, or is permitted to issue, share capital as set forth or incorporated in the Time of Sale Prospectus and all of the issued and outstanding Company Shares have been duly and validly authorized and issued and are fully paid and non-assessable.

(k)(i) The Shares have been duly authorized and issued, and when delivered and paid for in accordance with the terms of this Agreement, will be validly issued, fully paid and non-assessable, and any legal requirements as to subscription or similar rights on such Shares have been validly complied with; (ii) the Shares, when delivered and paid for in the manner contemplated by this Agreement, will be subject only to any restrictions applicable under the Company’s Articles of Association, will be freely transferable and will not be subject to any third party rights of any nature; and (iii) the Shares, when delivered and paid for in the manner contemplated by this Agreement, will belong to the same series and class as the issued share capital of the Company, granting the same voting and economic rights.

(l)Except, in each case, as set forth in the Prospectus, there are no stamp, issue, registration, documentary, sales, transfer, income, capital gains or other similar taxes or duties imposed under the laws of Switzerland or any political sub-division or taxing authority thereof or therein that is required to be paid in connection with (i) the execution, delivery, consummation or enforcement of this Agreement, (ii) the creation, allotment and issuance of the Shares, (iii) the sale and delivery of the Shares to the Underwriters or purchasers procured by the Underwriters, or (iv) the resale and delivery of the Shares by the Underwriters in the manner contemplated herein.

(m)Except as set forth or contemplated in the Prospectus, all dividends and other distributions declared and payable on the
Shares by the Company are not subject to withholding under the current laws and regulations of Switzerland or any political sub-division or taxing authority thereof or therein

(n)No consent, approval, authorization, order, registration or qualification of or with any court or governmental agency or body is required in connection with the execution, delivery and performance of this Agreement by the Company or the consummation of the transactions contemplated hereby and thereby, except (x) such as have been, or will be at the time of such issue and sale, including the issuance and sale of the Shares, obtained under the Securities Act of 1933, as amended (the “Securities Act”) and such consents, approvals, authorizations, registrations or qualifications as may be required under state securities or Blue Sky laws, (y) where the failure to possess such consent, approval, authorization, order, registration or qualification (A) would not, individually or in the aggregate, have a Material Adverse Effect, (B) would not impair the Company’s ability to perform its obligations hereunder or under the Registration Statement, the Time of Sale Prospectus and the Prospectus and (C) would not have any material adverse effect upon the consummation of the transactions contemplated hereby and thereby or (z) filings with the Commercial Register in the Canton of Zug in connection with the issuance of Shares.

(o)Neither the Company, nor any of its affiliates, nor any person acting on behalf of any of them (provided that the Company makes no representation as to actions of any Underwriter) has, directly or indirectly, made offers or sales of any security, or solicited offers to buy any security, under circumstances that would require the publication of a prospectus under the Swiss Financial Services Act (the “FinSA”) or under Regulation EU 2017/1129 of the European Parliament and of the Council on the prospectus to be published when securities are offered to the public or admitted to trading on a regulated market and repealing Directive 2003/71/EC (the “Prospectus Regulation”). Neither the Company, nor any of its affiliates, nor any person acting on behalf of any of them (provided that the Company makes no representation as to actions of any Underwriter) has engaged in any form of solicitation or advertising or in any directed selling efforts with respect to the Shares in Switzerland or any member state of the European Economic Area, except in circumstances permitted under the FinSA or the Prospectus Regulation, respectively.

(p)Other than as set forth in the Time of Sale Prospectus, there are no legal or governmental proceedings pending to which the Company or any of the Subsidiaries is a party or of which any property of the Company or any of the Subsidiaries is the subject, which, if determined adversely to the Company or any of the Subsidiaries, would, individually or in the aggregate, have a Material

Adverse Effect; and, to the Company’s knowledge, no such proceedings are threatened or contemplated by governmental authorities or threatened by others.

(q)None of the Company or any of the Subsidiaries is in violation of (i) its Articles of Association and Organizational Regulations, (ii) its Certificate of Incorporation or Bylaws, or equivalent documentation, as the case may be, or (iii) in default in the performance or observance of any material obligation, covenant or condition contained in any indenture, mortgage, deed of trust, loan agreement, lease or other agreement or instrument to which it is a party or by which it or any of its properties may be bound, except, in the case of clause (iii), for any such violation or default which would not, individually or in the aggregate, have a Material Adverse Effect.

(r)The Company is not and, after giving effect to the offer and sale of the Shares and the application of the proceeds thereof, will not be an “investment company,” as such term is defined in the Investment Company Act of 1940, as amended.

(s)Ernst & Young LLP, who have certified certain financial statements of the Company and the Subsidiaries and have audited the Company’s internal control over financial reporting are independent registered public accountants.

(t)The Company maintains a system of internal control over financial reporting (as such term is defined in Rule 13a-15(f) under the Exchange Act) that complies with the requirements of the Exchange Act and has been designed by the Company’s principal executive officer and principal financial officer, or under their supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles in the United States (“GAAP”). Management of the Company assessed its internal control over financial reporting as of December 31, 2024 and concluded internal control over financial reporting was effective as of such date. The Company is not aware of any material weaknesses in its internal control over financial reporting.

(u)(i) The Company and each of the Subsidiaries materially comply with all internal and external privacy policies authored by the Company (or the Subsidiaries), as well as any contractual obligations and applicable laws relating to the collection, use, transfer, import, export, storage, protection, disposal and disclosure by the Company or any of the Subsidiaries of personal data (“Data Security Obligations”, and such data, “Data”); (ii) the Company has not received any written notification of or complaint regarding any material violation by the Company or any of the Subsidiaries of any Data Security Obligation; and (iii) there is no action, suit or proceeding by or before any court or governmental

agency, authority or body pending or threatened alleging material non-compliance by the Company or any of the Subsidiaries with any Data Security Obligation.

(v)The Company and each of the Subsidiaries have taken commercially reasonable technical and organizational measures to protect the information technology systems and Data used in connection with the operation of the Company’s and the Subsidiaries’ businesses. Without limiting the foregoing, the Company and the Subsidiaries have used reasonable efforts to establish and maintain reasonable information technology, information security, cyber security and data protection controls, policies and procedures, including business continuity/disaster recovery and security plans that are designed to protect against and prevent unauthorized breach, destruction, loss, use, access, disablement, misappropriation or modification of an information technology system or Data used in connection with the operation of the Company’s and the Subsidiaries’ businesses (“Breach”). In the past three years, there has been no material Breach, and the Company and the Subsidiaries have not been notified of and have no knowledge of any event or condition that would reasonably be expected to result in, any material Breach.

(w)Except as disclosed in the Registration Statement or the Time of Sale Prospectus, since the date of the latest audited financial statements included or incorporated by reference in each of the Registration Statement or the Time of Sale Prospectus, there has been no change in the Company’s internal control over financial reporting that has materially affected, or is reasonably likely to materially affect, the Company’s internal control over financial reporting.

(x)The Company maintains disclosure controls and procedures (as such term is defined in Rule 13a-15(e) under the Exchange Act) that comply with the requirements of the Exchange Act; such disclosure controls and procedures have been designed to ensure that information required to be disclosed by the Company in the reports that it files or submits under the Exchange Act (including related interactive data in eXtensible Business Reporting Language) is accumulated and communicated to the Company’s management and such disclosure controls and procedures were effective as of December 31, 2024.

(y)Prior to the date of this Agreement, neither the Company nor any of its affiliates have taken any action which is designed to or which has constituted, or which might have been expected to cause or result in, the stabilization or manipulation of the price of any security of the Company in connection with the offer and sale of the Shares.

(z)The Company is in compliance with the requirements of all applicable laws of governmental authorities having jurisdiction over its operations and all orders, writs, injunctions and decrees of such governmental authorities applicable to it, Transocean International Limited, Transocean Holdings 1 Limited, Transocean Holdings 2 Limited, Transocean Holdings 3 Limited or any

of their respective properties, except where (i) any such non-compliance, individually or in the aggregate, would not reasonably be expected to result in a Material Adverse Effect, or (ii) the Company is contesting such law, order, writ, injunction or decree in good faith by appropriate proceedings and reserves in conformity with GAAP have been provided therefor as applicable.

(aa)Except as disclosed in the Time of Sale Prospectus, there exists no action, suit, investigation, litigation or proceeding pending or, to the knowledge of the Company, threatened against the Company or the Subsidiaries that has had, or could reasonably be expected to have, a Material Adverse Effect.

(bb)Except as would not, individually or in the aggregate, have a Material Adverse Effect on the Company and the Subsidiaries, taken as a whole, or except as described in the Time of Sale Prospectus: (i) the Company and the Subsidiaries and their respective operations and facilities are in compliance with, and not subject to any known liabilities under, applicable Environmental Laws (as defined below), which compliance includes, without limitation, having obtained, and being in compliance with all permits, licenses or other governmental authorizations or approvals, and having made all filings and provided all financial assurances and notices, required for the ownership and operation of the business, properties and facilities of the Company or the Subsidiaries under applicable Environmental Laws, and compliance with the terms and conditions thereof; (ii) neither the Company nor any of the Subsidiaries has received any written communication, whether from a governmental authority, citizens group, employee or otherwise, that alleges that the Company or any of the Subsidiaries is in violation of any Environmental Law; (iii) there is no claim, action or cause of action filed with a court or governmental authority, no investigation with respect to which the Company has received written notice, and no written notice by any person or entity alleging actual or potential liability on the part of the Company or any of the Subsidiaries based on or pursuant to any Environmental Law pending or, to the best of the Company’s knowledge, threatened against the Company or any of the Subsidiaries or any person or entity whose liability under or pursuant to any Environmental Law, the Company or any of the Subsidiaries has retained or assumed either contractually or by operation of law; (iv) neither the Company nor any of the Subsidiaries is conducting or paying for, in whole or in part, any investigation, response or other corrective action pursuant to any Environmental Law at any site or facility, nor is any of them subject or a party to any order, judgment, decree, contract or agreement which imposes any obligation or liability under any Environmental Law; (v) no lien, charge, encumbrance or restriction has been recorded pursuant to any Environmental Law with respect to any assets, facility or property owned, operated or leased by the Company or any of the Subsidiaries; and (vi) there are no past or present actions, activities, circumstances, conditions or occurrences including, without limitation, the Release (as defined below) or threatened Release of any Material of Environmental Concern (as defined below), that could result in a violation of or

liability under any Environmental Law on the part of the Company or any of the Subsidiaries including, without limitation, any such liability which the Company or any of the Subsidiaries has retained or assumed either contractually or by operation of law.

For purposes of this Agreement, “Environment” means ambient air, indoor air, surface water, groundwater, drinking water, soil, surface and subsurface strata, and natural resources such as wetlands, flora and fauna. “Environmental Laws” means the common law and all federal, state, local and foreign laws, rules or regulations, ordinances, codes, orders, decrees, judgments and injunctions issued, promulgated or entered thereunder, relating to pollution or protection of the Environment or occupational health and workplace safety including without limitation, those relating to (i) the Release or threatened Release of Materials of Environmental Concern; and (ii) the manufacture, processing, distribution, use, generation, treatment, storage, transport or disposal or arrangement for transport or disposal, handling or recycling of Materials of Environmental Concern. “Materials of Environmental Concern” means (i) any substance, material, pollutant, contaminant, chemical, waste, compound, or constituent, in any form subject to regulation or which can give rise to liability under any Environmental Law. “Release” means any releasing, spilling, emitting, discharging, depositing, disposing, leaking, pumping, pouring, dumping, emptying, injecting, escaping, migrating or leaching into the Environment, or into, from or through any building, structure or facility.

(cc)In the ordinary course of its business, the Company conducts a periodic review of the effect of Environmental Laws on the business, operations and properties of the Company and the Subsidiaries, in the course of which it identifies and evaluates associated costs and liabilities (including, without limitation, any capital or operating expenditures required for clean-up, closure of properties or compliance with Environmental Laws or any permit, license or approval, any related constraints on operating activities and any potential liabilities to third parties). On the basis of such review and the amount of its established reserves, the Company has reasonably concluded that such associated costs and liabilities would not, individually or in the aggregate, have a material effect on the Company and the Subsidiaries, taken as a whole.

(dd)(i) Neither the Company nor any of its Subsidiaries or affiliates, nor any director or officer nor, to the Company’s knowledge, any employee, agent or representative of the Company or of any of its Subsidiaries or affiliates, has taken or will take any action in furtherance of an offer, payment, promise to pay, or authorization or approval of the payment, giving or receipt of money, property, gifts or anything else of value, directly or indirectly, to any “government official” (including any officer or employee of a government or government-owned or controlled entity or of a public international organization, or any person acting in an official capacity for or on behalf of any of the foregoing, or any political party or party official or candidate for political office) to influence official action or

secure an improper advantage in violation of (a) the U.S. Foreign Corrupt Practices Act of 1977, (b) the UK Bribery Act 2010, and (c) any other applicable law or regulation relating to bribery or corruption (collectively, the “Anti-Corruption Laws”); (ii) the Company and its Subsidiaries and affiliates have conducted their businesses in compliance with applicable Anti-Corruption Laws and have instituted and maintained and will continue to maintain policies and procedures reasonably designed to promote and achieve compliance with such laws and with the representation and warranty contained herein; and except as disclosed in the Time of Sale Prospectus, no investigation, action, suit or proceeding by or before any court or governmental agency, authority or body or any arbitrator involving the Company or any of its Subsidiaries or affiliates, nor any director, officer, or employee of the same, with respect to the Anti-Corruption Laws is, to the knowledge of the Company, pending or threatened; and (iii) neither the Company nor any of the Subsidiaries will use, directly or indirectly, the proceeds of the offering in furtherance of an offer, payment, promise to pay, or authorization of the payment or giving of money, or anything else of value, to any person in violation of any applicable Anti-Corruption Laws.

(ee)The operations of the Company and the Subsidiaries are and have been conducted at all times in material compliance with all applicable financial recordkeeping and reporting requirements, including those of the Bank Secrecy Act, as amended by Title III of the Uniting and Strengthening America by Providing Appropriate Tools Required to Intercept and Obstruct Terrorism Act of 2001 (USA PATRIOT Act), and the applicable anti-money laundering statutes of jurisdictions where the Company and the Subsidiaries conduct business, the rules and regulations thereunder and any related or similar rules, regulations or guidelines, issued, administered or enforced by any governmental agency including the Money Laundering Control Act of 1986, and the Anti-Money Laundering Act of 2020 (collectively, the “Anti-Money Laundering Laws”), and no investigation, inquiry, action, suit or proceeding by or before any court or governmental agency, authority or body or any arbitrator involving the Company or any of the Subsidiaries or any directors, officers, or employees of the same, with respect to the Anti-Money Laundering Laws is pending or, to the knowledge of the Company, threatened. Neither the Company nor any of the Subsidiaries will use, directly or indirectly, the proceeds of the offering in any manner in violation of any applicable Anti-Money Laundering Laws.

(ff)(i)Neither the Company nor any of the Subsidiaries, nor any director nor officer nor employee thereof, nor, to the Company’s knowledge, any agent, affiliate or representative of the Company or any of its Subsidiaries, is an individual or entity (“Person”) that is, or is directly or indirectly owned or otherwise controlled by a Person that is:

●

the subject of any sanctions administered or enforced by the United States Government (including the U.S. Department of Treasury’s

Office of Foreign Assets Control, the U.S. Department of State, the U.S. Department of Commerce’s Bureau of Industry and Security), the United Nations Security Council, the European Union, His Majesty’s Treasury, the Swiss State Secretariat for Economic Affairs or the Swiss Directorate of International Law or any other relevant sanctions authority (collectively, “Sanctions”), nor

●

located, organized or resident in a country or territory, or a national of a country or territory, that is the subject of comprehensive Sanctions, which may change from time to time (including, without limitation, the Crimea, Kherson, and Zaporizhzhia regions of Ukraine, the so-called Donestk People’s Republic and the so-called Luhansk People’s Republic, Cuba, Iran, North Korea and Syria); provided that with regards to employee location, a breach of this representation shall only be deemed to have occurred to the extent that such location, organization, residence or nationality would expose the Company, any of its Subsidiaries, or the Underwriters to liability or penalty under, or otherwise result in the Company, any of its Subsidiaries or the Underwriters being in violation of or becoming the target of applicable Sanctions.

(ii) The Company will not, directly or indirectly, use the proceeds of the sale of any Shares, or lend, contribute or otherwise make available such proceeds to any of the Subsidiaries, joint venture partners or other Persons:

●to fund or facilitate any activities or business of or with any Person or in any country or territory that, at the time of such funding or facilitation, is or whose government is, the subject of Sanctions, except as authorized for all relevant parties under applicable Sanctions; or

●in any other manner that will result in (i) a violation of Sanctions by any Person or (ii) any person becoming the target of sanctions (including any Person participating in the offering, whether as initial purchaser, underwriter, advisor, investor or otherwise).

(iii)

Since April 24, 2019, the Company and its Subsidiaries have not knowingly engaged in, are not now knowingly engaged in, and will not engage in, any dealings or transactions with any Person, or in any country or territory, that at the time of the dealing or transaction is or was the subject of Sanctions, in each case in violation of applicable Sanctions.

(iv)

The Company and its Subsidiaries have instituted and maintained and will continue to maintain policies and procedures reasonably designed to promote and achieve compliance with Sanctions, and

except as disclosed in the Time of Sale Prospectus, no action, suit, investigation, inquiry or proceeding by or before any court or governmental agency, authority or body or any arbitrator involving the Company or any of the Subsidiaries or its affiliates, nor any director, officer, or employee of the same, with respect to Sanctions is pending, or to the knowledge of the Company, pending or threatened.

(gg)The financial statements, together with the related schedules and notes, included or incorporated by reference in the Registration Statement, the Time of Sale Prospectus and the Prospectus present fairly the consolidated financial position of the entities to which they relate as of and at the dates indicated and the results of their operations and cash flows for the periods specified. Such financial statements have been prepared in accordance with GAAP applied on a consistent basis throughout the periods involved, except as may be expressly stated in the related notes thereto. The other financial information included or incorporated by reference in each of the Registration Statement, the Time of Sale Prospectus and the Prospectus has been derived from the accounting records of the Company and the Subsidiaries and presents fairly in all material respects the information shown thereby. The statistical and market related data and forward looking statements included or incorporated by reference in the Registration Statement, the Time of Sale Prospectus and the Prospectus are based on or derived from sources that the Company believes to be reliable and accurate in all material respects and represents their good faith estimates that are made on the basis of data derived from such sources.

(hh)The Company and the Subsidiaries own or possess, or can acquire on reasonable terms, all patents, patent rights, licenses, inventions, copyrights, know how (including trade secrets and other unpatented and/or unpatentable proprietary or confidential information, systems or procedures), trademarks, service marks and trade names currently employed by them in connection with or otherwise necessary for the business now operated by them, except where the failure to so own or possess would not have a Material Adverse Effect, and neither the Company nor any of the Subsidiaries has infringed, is infringing or has received any notice of infringement of or conflict with asserted rights of others with respect to any of the foregoing which, singly or in the aggregate, except as would not have a Material Adverse Effect on the Company and the Subsidiaries, taken as a whole.

(ii)The Company and the Subsidiaries possess, and to the extent required, have timely filed applications to renew, and are operating in compliance in all material respects with, all franchises, grants, authorizations, licenses, permits, easements, consents, certificates and orders of any governmental authority or self-regulatory body required for the conduct of their respective businesses and all such franchises, grants, authorizations, licenses, permits,

easements, consents, certificates and orders are valid and in full force and effect, except where the failure to so possess or operate in compliance would not have a Material Adverse Effect, and neither the Company nor the Subsidiaries have received notice of any revocation or modification of any such franchise, grant, authorization, license, permit, easement, consent, certification or order or has reason to believe that any such franchise, grant, authorization, license, permit, easement, consent, certification or order will not be renewed in the ordinary course, except where such revocation, modification or non-renewal would not have a Material Adverse Effect; and the Company and the Subsidiaries are in compliance in all material respects with all applicable federal, state, local and foreign laws, regulations, orders and decrees, except where such non-compliance would not have a Material Adverse Effect on the Company and the Subsidiaries, taken as a whole, except as described in the Time of Sale Prospectus.

(jj)The Company and the Subsidiaries have good title to or a valid leasehold interest in all of their real property and good title to or a valid leasehold interest in all of their other property, except where the failure to have such title or leasehold interest in such property could not have a Material Adverse Effect.

(kk)The Company and the Subsidiaries have filed all U.S. federal, state, local and non-U.S. tax returns required to be filed through the date of this Agreement or have requested extensions thereof (except where the failure to file would not, individually or in the aggregate, have a Material Adverse Effect) and have paid all taxes (except for cases in which the failure to pay would not, individually or in the aggregate, have a Material Adverse Effect, or, except as currently being contested in good faith and for which reserves, to the extent required by GAAP have been created in the financial statements of the Company). No tax deficiency has been determined adversely to the Company or the Subsidiaries which has had (nor does the Company nor any of the Subsidiaries have any notice or knowledge of any tax deficiency which could be determined adversely to the Company or the Subsidiaries and which could have) a Material Adverse Effect.

(ll)The Company and the Subsidiaries are insured by insurers of recognized financial responsibility against such losses and risks and in such amounts as the Company reasonably believes to be prudent and customary in the businesses in which they are engaged; neither the Company nor the Subsidiaries have been refused any insurance coverage sought or applied for; and neither the Company nor any Subsidiary has any reason to believe that it will not be able to renew its existing insurance coverage as and when such coverage expires or to obtain similar coverage from similar insurers as may be necessary to continue its business at a cost that would not have a Material Adverse Effect, except as described in the Time of Sale Prospectus.

(mm)The Company and the Subsidiaries and their respective officers and directors are in compliance with the applicable provisions of the Sarbanes-

Oxley Act of 2002 (the “Sarbanes-Oxley Act,” which term, as used herein, includes the rules and regulations of the Commission promulgated thereunder).

(nn)The Company and the Subsidiaries and any “employee benefit plan” (as defined under the Employee Retirement Income Security Act of 1974 (as amended, “ERISA,” which term, as used herein, includes the regulations and published interpretations thereunder)) established, maintained or contributed to by the Company and the Subsidiaries or their “ERISA Affiliates” (as defined below) are in compliance in all respects with ERISA except for any such non-compliance which would not reasonably be expected to result in a Material Adverse Effect. “ERISA Affiliate” means, with respect to the Company and the Subsidiaries, any member of any group of organizations described in Section 414 of the Internal Revenue Code of 1986 (as amended, the “Code,” which term, as used herein, includes the regulations and published interpretations thereunder) of which the Company and the Subsidiaries are a member. No “reportable event” (as defined under ERISA) has occurred or is reasonably expected to occur with respect to any “employee benefit plan” established, maintained or contributed to by the Company, the Subsidiaries or any of their ERISA Affiliates, which would result in a Material Adverse Effect. No “employee benefit plan” established, maintained or contributed to by the Company or the Subsidiaries or any of their ERISA Affiliates, if such “employee benefit plan” were terminated, would have any “amount of unfunded benefit liabilities” (as defined under ERISA) that would result in a Material Adverse Effect. Neither the Company nor the Subsidiaries nor any of their ERISA Affiliates has incurred or reasonably expects to incur any liability under (i) Title IV of ERISA with respect to termination of, or withdrawal from, any “employee benefit plan” or (ii) Sections 412, 4971, 4975 or 4980B of the Code, which would result in a Material Adverse Effect. Each “employee benefit plan” established or maintained by the Company or the Subsidiaries or any of their ERISA Affiliates that has been determined by the Internal Revenue Service to be qualified under Section 401 of the Code is so qualified and nothing has occurred, whether by action or failure to act, which would cause the loss of such qualification.

(oo)Except as described in the Registration Statement, the Time of Sale Prospectus or the Prospectus, there are no contracts, agreements or understandings between the Company and any person granting such person the right to require the Company to file a registration statement under the Securities Act with respect to any securities of the Company or to require the Company to include such securities with the Shares registered pursuant to the Registration Statement.

2.Agreement to Sell and Purchase.

(a)Subject to the terms and conditions and in reliance upon the basis of the representations and warranties herein set forth, the Company agrees to issue and sell to each of the Underwriters, and each of the Underwriters agrees, severally and not jointly, to purchase from the Company the number of Firm

Shares set forth in Schedule I hereto opposite the name of such Underwriter at $2.93 per share (the “Purchase Price”); provided that with respect to up to 4,000,000 Firm Shares that may be sold by the Underwriters to certain of the Company’s directors, including entities affiliated with them, it is agreed the Purchase Price shall be $3.05 per share.

(b)Subject to the terms and conditions and in reliance upon the representations and warranties herein set forth, the Company grants an option to the Underwriters to purchase, severally and not jointly, up to 18,750,000 Additional Shares at the Purchase Price, provided, however, that the amount paid by the Underwriters for any Additional Shares shall be reduced by an amount per share equal to any dividends declared by the Company and payable on the Firm Shares but not payable on such Additional Shares. The Representatives may exercise this right on behalf of the Underwriters in whole or from time to time in part by giving written notice not later than 30 days after the date of this Agreement. Any exercise notice shall specify the number of Additional Shares to be purchased by the Underwriters and the date on which such shares are to be purchased. Each purchase date must be at least one business day after the written notice is given and may not be earlier than the closing date for the Firm Shares or later than ten business days after the date of such notice. On each day, if any, that Additional Shares are to be purchased (an “Option Closing Date”), each Underwriter agrees, severally and not jointly, to purchase the number of Additional Shares (subject to such adjustments to eliminate fractional shares as the Representatives may determine) that bears the same proportion to the total number of Additional Shares to be purchased on such Option Closing Date as the number of Firm Shares set forth in Schedule I hereto opposite the name of such Underwriter bears to the total number of Firm Shares.

3.Payment and Delivery. Payment for the Firm Shares shall be made to the Company in Federal or other funds immediately available in New York City against delivery of such Shares for the account of the Underwriters at 10:00 a.m., New York City time, on September 26, 2025, and, with respect to the Additional Shares, 10:00 a.m., New York City time, on the date specified by the Representatives in the written notice given by the Representatives’ election to purchase such Additional Shares or at such other time on the same or such other date, not later than October 24, 2025, as shall be designated in writing by the Underwriters. The time and date of such payment are hereinafter referred to as the “Closing Date.”

The Shares shall be registered in such names and in such denominations as the Underwriters shall request not later than one full business day prior to the Closing Date. The Shares shall be delivered to the Underwriters on the Closing Date, for the respective account of the Underwriters, with any transfer or other similar taxes payable in connection with the transfer of the Shares to the Underwriters duly paid, against payment of the Purchase Price therefor.

4.Conditions to the Underwriters’ Obligations. The obligation of the Company to sell the Shares to the Underwriters and the obligation of the Underwriters to purchase and pay for the Shares on the Closing Date are subject to the condition that the Registration Statement became effective prior to the execution of this Agreement.

The obligation of the Underwriters is subject to the following further conditions:

(a)Subsequent to the execution and delivery of this Agreement and prior to the Closing Date:

(i)no order suspending the effectiveness of the Registration Statement shall be in effect, and no proceeding for such purpose or pursuant to Section 8A under the Securities Act shall be pending before or threatened by the Commission;

(ii)there shall not have occurred any downgrading, nor shall any notice have been given of any intended or potential downgrading or of any review for a possible change that does not indicate the direction of the possible change, in the rating accorded the Company or any of the securities of the Company or Transocean International Limited by any “nationally recognized statistical rating organization,” as such term is defined in Section 3(a)(62) of the Exchange Act; and

(iii)there shall not have occurred any change, or any development involving a prospective change, in the condition, financial or otherwise, or in the earnings, business or operations of the Company and the Subsidiaries, taken as a whole, from the date of the Time of Sale Prospectus that, in the Underwriters’ reasonable judgment, is material and adverse and that makes it, in the Underwriters’ reasonable judgment, impracticable to market the Shares on the terms and in the manner contemplated in the Time of Sale Prospectus.

(b)The Underwriters shall have received on the Closing Date a certificate, dated the Closing Date and signed by an executive officer of the Company, to the effect set forth in Sections 4(a)(i) and 4(a)(ii) above and to the effect that the representations and warranties of the Company contained in this Agreement were true and correct in all material respects as of the Time of Sale and are true and correct in all material respects (unless such representation or warranty is already so qualified) as of the Closing Date and that the Company has complied with all of the agreements and satisfied all of the conditions on its part to be performed or satisfied hereunder on or before the Closing Date.

The officer signing and delivering such certificate may rely upon the best of his or her knowledge as to proceedings threatened.

(c)The Underwriters shall have received on the Closing Date, an opinion and negative assurance letter of Baker Botts L.L.P., outside counsel for the Company, dated such date, substantially to the effect set forth in Exhibit B hereto.

(d)The Underwriters shall have received on the Closing Date, an opinion of Homburger AG, Swiss counsel for the Company, dated such date, substantially to the effect set forth in Exhibit C hereto.

(e)The Underwriters shall have received on the Closing Date, an opinion and a negative assurance letter of Baker McKenzie, LLP, special tax counsel for the Company, dated such date, substantially to the effect set forth in Exhibit D hereto.

(f)The Underwriters shall have received on the Closing Date, an opinion and a negative assurance letter of Vinson & Elkins, L.L.P., counsel for the Underwriters, dated such date, in form and substance reasonably satisfactory to the Underwriters.

The opinion of counsel for the Company described in Section 4(c), Section 4(d) and Section 4(e) above shall be rendered to the Underwriters at the request of the Company and shall so state therein.

(g)The Underwriters shall have received on each of the date hereof and the Closing Date, a letter dated such date in form and substance reasonably satisfactory to the Underwriters, from Ernst & Young LLP, independent public accountants for the Company, confirming that they are an independent registered public accounting firm within the meaning of the Securities Act, the Exchange Act and the Public Company Accounting Oversight Board, stating, as of such date, the conclusions and findings of such firm with respect to the financial information and other matters ordinarily covered by accountants’ “comfort letters” to underwriters in connection with registered public offerings; provided that the letter delivered on the Closing Date shall use a “cut-off date” not earlier than the date hereof.

(h)The “lock up” agreements, each substantially in the form of Exhibit A hereto, between the Representatives and the officers and directors of the Company listed in Exhibit E relating to restrictions on sales and certain other dispositions of Company Shares or certain other securities, delivered to the Underwriters on or before the date hereof, shall be in full force and effect on the Closing Date.

(i)The Shares shall have been approved for listing on the New York Stock Exchange (“NYSE”), subject only to a notice of issuance at or prior to the Closing Date.

(j)The Shares, when delivered and paid for in accordance with the terms of this Agreement, shall have been duly and validly authorized and issued and, to the extent required under applicable Swiss law, registered with the Commercial Register of the Canton of Zug.

(k)The several obligations of the Underwriters to purchase Additional Shares hereunder are subject to the delivery to the Representatives on the applicable Option Closing Date of the following:

(A)a certificate, dated the Option Closing Date and signed by an executive officer of the Company, confirming that the certificate delivered on the Closing Date pursuant to Section 4(b) hereof remains true and correct as of such Option Closing Date;

(B)an opinion and negative assurance letter of Baker Botts L.L.P., outside counsel for the Company, dated the Option Closing Date, relating to the Additional Shares to be purchased on such Option Closing Date and otherwise to the same effect as the opinion required by Section 4(c) hereof;

(C)an opinion and a negative assurance letter of Baker McKenzie, LLP, special tax counsel for the Company, dated the Option Closing Date, relating to the Additional Shares to be purchased on such Option Closing Date and otherwise to the same effect as the opinion required by Section 4(e) hereof;

(D)an opinion and negative assurance letter of Vinson & Elkins L.L.P., counsel for the Underwriters, dated the Option Closing Date, relating to the Additional Shares to be purchased on such Option Closing Date and otherwise to the same effect as the opinion required by Section 4(f) hereof;

(E)a letter dated the Option Closing Date, in form and substance satisfactory to the Underwriters, from Ernst & Young, independent public accountants for the Company, substantially in the same form and substance as the letter furnished to the Underwriters pursuant to Section 4(g) hereof; provided that the letter delivered on the Option Closing Date shall use a “cut-off date” not earlier than two business days prior to such Option Closing Date; and

(F) such other documents as the Representatives may reasonably request with respect to the due authorization and issuance of the Additional Shares to be sold on such Option Closing Date.

5.Covenants of the Company. The Company covenants with each of the Underwriters as follows:

(a)To furnish to the Underwriters, without charge, as many signed copies of the Registration Statement (including exhibits thereto and documents incorporated by reference) as the Underwriters may reasonably request and to furnish to the Underwriters in New York City, without charge, prior to 10:00 a.m. New York City time on the business day next succeeding the date of this Agreement and during the period mentioned in Section 5(e) ‎ or 5(f) below, as many copies of the Time of Sale Prospectus, the Prospectus, any documents incorporated by reference therein and any supplements and amendments thereto or to the Registration Statement as the Underwriters may reasonably request.

(b)Before amending or supplementing the Registration Statement, the Time of Sale Prospectus or the Prospectus, to furnish to the Underwriters a copy of each such proposed amendment or supplement and not to file any such proposed amendment or supplement to which the Underwriters reasonably object, and to file with the Commission within the applicable period specified in Rule 424(b) under the Securities Act any prospectus required to be filed pursuant to such Rule.

(c)To furnish to the Underwriters a copy of each proposed free writing prospectus to be prepared by or on behalf of, used by, or referred to by the Company and not to use or refer to any proposed free writing prospectus to which the Underwriters reasonably object.

(d)Not to take any action that would result in the Underwriters or the Company being required to file with the Commission pursuant to Rule 433(d) under the Securities Act a free writing prospectus prepared by or on behalf of the Underwriters that the Underwriters otherwise would not have been required to file thereunder.

(e)If the Time of Sale Prospectus is being used to solicit offers to buy the Shares at a time when the Prospectus is not yet available to prospective purchasers and any event shall occur or condition exist as a result of which it is necessary to amend or supplement the Time of Sale Prospectus in order to make the statements therein, in the light of the circumstances under which they were made, not misleading, or if any event shall occur or condition exist as a result of which the Time of Sale Prospectus conflicts with the information contained in the Registration Statement then on file, or if, in the opinion of counsel for the Underwriters, it is necessary to amend or supplement the Time of Sale Prospectus to comply with applicable law, forthwith to prepare, file with the Commission and furnish, at its own expense, to the Underwriters and to any dealer upon request, either amendments or supplements to the Time of Sale Prospectus so that the statements in the Time of Sale Prospectus as so amended or supplemented will not, in the light of the circumstances when the Time of Sale Prospectus is

delivered to a prospective purchaser, be misleading or so that the Time of Sale Prospectus, as amended or supplemented, will no longer conflict with the Registration Statement, or so that the Time of Sale Prospectus, as amended or supplemented, will comply with applicable law.

(f)If, during such period after the first date of the public offering of the Shares as in the opinion of counsel for the Underwriters the Prospectus (or in lieu thereof the notice referred to in Rule 173(a) of the Securities Act) is required by law to be delivered in connection with sales by the Underwriters or dealer, any event shall occur or condition exist as a result of which it is necessary to amend or supplement the Prospectus in order to make the statements therein, in the light of the circumstances when the Prospectus (or in lieu thereof the notice referred to in Rule 173(a) of the Securities Act) is delivered to a purchaser, not misleading, or if, in the opinion of counsel for the Underwriters, it is necessary to amend or supplement the Prospectus to comply with applicable law, forthwith to prepare, file with the Commission and furnish, at its own expense, to the Underwriters and to the dealers (whose names and addresses the Underwriters will furnish to the Company) to which Shares may have been sold by the Underwriters and to any other dealers upon request, either amendments or supplements to the Prospectus so that the statements in the Prospectus as so amended or supplemented will not, in the light of the circumstances when the Prospectus (or in lieu thereof the notice referred to in Rule 173(a) of the Securities Act) is delivered to a purchaser, be misleading or so that the Prospectus, as amended or supplemented, will comply with applicable law.

(g)To endeavor to qualify the Shares for offer and sale under the securities or Blue Sky laws of such jurisdictions as the Underwriters shall reasonably request; provided that in no event shall the Company be obligated to qualify to do business in any jurisdiction where it is not now so qualified or to take any action that would be subject it to service of process in suits, other than those arising out of the offering or sale of the Shares, or subject itself to taxation, in each case in any jurisdiction where it is not now so subject.

(h)To make generally available to the Company’s security holders and to the Underwriters as soon as practicable an earnings statement covering a period of at least twelve months beginning with the first fiscal quarter of the Company occurring after the date of this Agreement which shall satisfy the provisions of Section 11(a) of the Securities Act and the rules and regulations of the Commission thereunder.

(i)Whether or not the transactions contemplated in this Agreement are consummated or this Agreement is terminated, to pay or cause to be paid all expenses incident to the performance of its obligations under this Agreement, including: (i) the fees, disbursements and expenses of the Company’s counsel and the Company’s accountants in connection with the registration and delivery of the Shares under the Securities Act and all other fees or expenses in connection

with the preparation and filing of the Registration Statement, the Preliminary Prospectus, the Time of Sale Prospectus, the Prospectus, any free writing prospectus prepared by or on behalf of, used by, or referred to by the Company and amendments and supplements to any of the foregoing, including the filing fees payable to the Commission relating to the Shares (within the time required by Rule 456(b)(1), if applicable), all printing costs associated therewith, and the mailing and delivering of copies thereof to the Underwriters, in the quantities hereinabove specified, (ii) all costs and expenses related to the transfer and delivery of the Shares to the Underwriters, including any transfer or other taxes payable thereon, the cost of printing or producing any Blue Sky or Legal Investment memorandum in connection with the offer and sale of the Shares under state securities laws and all expenses in connection with the qualification of the Shares for offer and sale under state securities laws as provided in Section ‎5(g) hereof, including filing fees and the reasonably incurred and documented fees and disbursements of counsel for the Underwriters in connection with such qualification and in connection with the Blue Sky or Legal Investment memorandum, (iii) all filing fees and the reasonable fees and disbursements of counsel to the Underwriters incurred in connection with the review and qualification of the offering of the Shares by the Financial Industry Regulatory Authority (provided that the amount payable by the Company with respect to fees and disbursements of counsel for the Underwriters pursuant to subsections (ii) and (iii) shall not exceed $25,000 in the aggregate), (iv) all costs and expenses incident to listing the Shares on the NYSE and other national securities exchanges and foreign stock exchanges, (v) the cost of printing certificates representing the Shares, (vi) the costs and charges of any transfer agent, registrar or depositary of the Company, (vii) the costs and expenses of the Company relating to investor presentations on any “road show” undertaken in connection with the marketing of the offering of the Shares, including, without limitation, expenses associated with the preparation or dissemination of any electronic road show, expenses associated with the production of road show slides and graphics, fees and expenses of any consultants engaged in connection with the road show presentations with the prior approval of the Company, (viii) the document production charges and expenses associated with printing this Agreement, and (ix) all other costs and expenses incident to the performance of the obligations of the Company hereunder for which provision is not otherwise made in this Section 5. It is understood, however, that except as provided in this Section 5, Section ‎7 entitled “Indemnity and Contribution” and the last paragraph of Section ‎10 below, the Underwriters will pay all of their costs and expenses, including fees and disbursements of their counsel, stock transfer taxes payable on resale of any of the Shares by them and any advertising expenses connected with any offers they may make.

(j)The Company will deliver to the Underwriters (or its agent), on the date of execution of this Agreement, a properly completed and executed Certification Regarding Beneficial Owners of Legal Entity Customers, together with copies of identifying documentation, and the Company undertakes to provide

such additional supporting documentation as the Underwriters may reasonably request in connection with the verification of the foregoing Certification.

(k)The Company also covenants with each of the Underwriters that, without the prior written consent of the Representatives, it will not, during the period ending 60 days after the date of the Prospectus (the “Restricted Period”), (a) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, lend, or otherwise transfer or dispose of, directly or indirectly, any Company Shares or any securities convertible into or exercisable or exchangeable for Company Shares, excluding any exchangeable bonds issued by Transocean International Limited and guaranteed by the Company or any of its subsidiaries, or (b) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of the Company Shares, whether any such transaction described in clause (a) or (b) above is to be settled by delivery of Company Shares or such other securities, in cash or otherwise, (c) file any registration statement with the Commission relating to the offering of any Company Shares or any securities convertible into or exercisable or exchangeable for Company Shares (other than a registration statement on Form S-8 or any registration statement the Company is required to file pursuant to registration rights existing as of the date of this Agreement and, for the sake of clarity, other than any post-effective amendments to any registration statements effective as of the date of this Agreement) or (d) publicly disclose the intention to enter into any such transaction or make such filing. The restrictions contained in the foregoing sentence shall not apply to (A) the Shares to be sold hereunder, (B) the issuance by the Company of Company Shares upon the exercise of an option or warrant or the exchange or conversion of a security outstanding on the date hereof and described in each of the Time of Sale Prospectus and Prospectus, grants of employee stock options, stock appreciation rights, restricted units, deferred units and similar awards pursuant to the terms of a plan in effect on the date hereof (as any such plan may be amended from time to time) and issued or granted pursuant to a plan, agreement or other document described in the Time of Sale Prospectus and the Prospectus, or issuances of Company Shares pursuant to the exercise or vesting of such awards, or (C) facilitating the establishment of a trading plan on behalf of a shareholder, officer or director of the Company pursuant to Rule 10b5-1 under the Exchange Act, for the transfer of Company Shares; provided that (i) such plan does not provide for the transfer of Company Shares during the Restricted Period and (ii) to the extent a public announcement or filing under the Exchange Act, if any, is required of or voluntarily made by the Company regarding the establishment of such plan, such announcement or filing shall include a statement to the effect that no transfer of Company Shares may be made under such plan during the Restricted Period.

(l)The Company shall pay, and shall indemnify and hold the Underwriters harmless against, any stamp, issue, registration, documentary, sales,

transfer income, capital gains or other similar taxes or duties imposed under the laws of Switzerland or any political sub-division or taxing authority thereof or therein that is payable in connection with (i) the execution, delivery, consummation or enforcement of this Agreement, (ii) the creation, allotment and issuance of the Shares, (iii) the sale and delivery of the Shares to the Underwriters or purchasers procured by the Underwriters, or (iv) the resale and delivery of the Shares by the Underwriters in the manner contemplated herein.

(m) All sums payable by the Company under this Agreement shall be paid free and clear of and without deductions or withholdings of any present or future taxes or duties, unless the deduction or withholding is required by law, in which case the Company shall pay such additional amount as will result in the receipt by the Underwriters of the full amount that would have been received had no deduction or withholding been made.

(n)All sums payable to the Underwriters shall be considered exclusive of any value added or similar taxes. Where the Company is obliged to pay value added or similar tax on any amount payable hereunder to the Underwriters, the Company shall, in addition to the sum payable hereunder, pay an amount equal to any applicable value added or similar tax.

6.Covenants of the Underwriters. Each of the Underwriters covenants with the Company not to take any action that would result in the Company being required to file with the Commission under Rule 433(d) a free writing prospectus prepared by or on behalf of the Underwriters that otherwise would not be required to be filed by the Company thereunder, but for the action of the Underwriters.

7.Indemnity and Contribution. (a) The Company agrees to indemnify and hold harmless the Underwriters and their respective directors and officers, and each person, if any, who controls each Underwriter within the meaning of either Section 15 of the Securities Act or Section 20 of the Exchange Act and each affiliate of the Underwriters within the meaning of Rule 405 under the Securities Act from and against any and all losses, claims, damages and liabilities (including, without limitation, any reasonably incurred and documented legal or other expenses reasonably incurred and documented in connection with defending or investigating any such action or claim) that arise out of, or are based upon, any untrue statement or alleged untrue statement of a material fact contained in the Registration Statement, the Preliminary Prospectus, the Time of Sale Prospectus any free writing prospectus that the Company has filed, or is required to file, pursuant to Rule 433(d) under the Securities Act, any “road show” as defined in Rule 433(h) under the Securities Act (a “road show”), the Prospectus or any amendment or supplement to any such Registration Statement, Preliminary Prospectus, Time of Sale Prospectus, free writing prospectus, road show or Prospectus, or arise out of, or are based upon, any omission or alleged omission to state therein a material fact required to be stated therein or necessary

to make the statements therein not misleading, except insofar as such losses, claims, damages or liabilities arise out of, or are based upon, any such untrue statement or omission or alleged untrue statement or omission made in reliance upon and in conformity with any information relating to the Underwriters furnished to the Company in writing by the Underwriters expressly for use therein, it being understood and agreed that the only such information furnished by the Underwriters consists of the information described as such in paragraph (b) below.

(b)The Underwriters agree to indemnify and hold harmless the Company, its directors, its officers who sign the Registration Statement and each person, if any, who controls the Company within the meaning of either Section 15 of the Securities Act or Section 20 of the Exchange Act to the same extent as the foregoing indemnity from the Company to the Underwriter, but only with reference to information relating to the Underwriters furnished to the Company in writing by the Representatives expressly for use in the Registration Statement, the Preliminary Prospectus, the Time of Sale Prospectus, any free writing prospectus that the Company has filed, or is required to file, pursuant to Rule 433(d) under the Securities Act, any road show, the Prospectus or any amendment or supplement to any such Registration Statement, Preliminary Prospectus, Time of Sale Prospectus, free writing prospectus, road show or Prospectus, it being understood and agreed that the only such information furnished by the Underwriters consists of the following information in the Prospectus furnished on behalf of the Underwriters: the third paragraph, the twelfth paragraph and the list of Underwriters and their respective participation in the sale of the Shares under the caption “Underwriting (Conflicts of Interest)” under the caption “Underwriting.”

(c)In case any proceeding (including any governmental investigation) shall be instituted involving any person in respect of which indemnity may be sought pursuant to Section 7(a) or ‎7(b), such person (the “indemnified party”) shall promptly notify the person against whom such indemnity may be sought (the “indemnifying party”) in writing and the indemnifying party, upon request of the indemnified party, shall retain counsel reasonably satisfactory to the indemnified party to represent the indemnified party and any others the indemnifying party may designate in such proceeding and shall pay the reasonably incurred and reasonably documented fees and disbursements of such counsel related to such proceeding. In any such proceeding, any indemnified party shall have the right to retain its own counsel, but the fees and expenses of such counsel shall be at the expense of such indemnified party unless (i) the indemnifying party and the indemnified party shall have mutually agreed to the retention of such counsel, or (ii) the named parties to any such proceeding (including any impleaded parties) include both the indemnifying party and the indemnified party and representation of both parties by the same counsel would be inappropriate due to actual or potential differing interests between them. It is understood that the indemnifying

party shall not, in respect of the legal expenses of any indemnified party in connection with any proceeding or related proceedings in the same jurisdiction, be liable for the fees and expenses of more than one separate firm (in addition to any local counsel) for all such indemnified parties and that all such fees and expenses shall be reimbursed as they are incurred. Such firm shall be designated in writing by the Representatives, in the case of parties indemnified pursuant to Section 7(a), and by the Company, in the case of parties indemnified pursuant to Section 7(b). The indemnifying party shall not be liable for any settlement of any proceeding effected without its written consent, but if settled with such consent or if there be a final judgment for the plaintiff, the indemnifying party agrees to indemnify the indemnified party from and against any loss or liability by reason of such settlement or judgment. Notwithstanding the foregoing sentence, if at any time an indemnified party shall have requested an indemnifying party to reimburse the indemnified party for fees and expenses of counsel as contemplated by the second and third sentences of this paragraph, the indemnifying party agrees that it shall be liable for any settlement of any proceeding effected without its written consent if (i) such settlement is entered into more than 60 days after receipt by such indemnifying party of the aforesaid request and (ii) such indemnifying party shall not have reimbursed the indemnified party in accordance with such request prior to the date of such settlement. No indemnifying party shall, without the prior written consent of the indemnified party, effect any settlement of any pending or threatened proceeding in respect of which any indemnified party is or could have been a party and indemnity could have been sought hereunder by such indemnified party, unless such settlement includes an unconditional release of such indemnified party from all liability on claims that are the subject matter of such proceeding.

(d)To the extent the indemnification provided for in Section 7(a) or ‎7(b) is unavailable to an indemnified party or insufficient in respect of any losses, claims, damages or liabilities referred to therein, then each indemnifying party under such paragraph, in lieu of indemnifying such indemnified party thereunder, shall contribute to the amount paid or payable by such indemnified party as a result of such losses, claims, damages or liabilities (i) in such proportion as is appropriate to reflect the relative benefits received by the Company on the one hand and the Underwriters on the other hand from the offering of the Shares or (ii) if the allocation provided by clause ‎ (i) above is not permitted by applicable law, in such proportion as is appropriate to reflect not only the relative benefits referred to in clause (i) but also the relative fault of the Company on the one hand and of the Underwriters on the other hand in connection with the statements or omissions that resulted in such losses, claims, damages or liabilities, as well as any other relevant equitable considerations. The relative benefits received by the Company on the one hand and the Underwriters on the other hand in connection with the offering of the Shares shall be deemed to be in the same respective proportions as the net proceeds from the offering of the Shares (before deducting expenses) received by the Company and the total underwriting discounts and

commissions received by the Underwriters. The relative fault of the Company on the one hand and the Underwriters on the other hand shall be determined by reference to, among other things, whether the untrue or alleged untrue statement of a material fact or the omission or alleged omission to state a material fact relates to information supplied by the Company or by the Underwriters and the parties’ relative intent, knowledge, access to information and opportunity to correct or prevent such statement or omission.

(e)The Company and the Underwriters agree that it would not be just or equitable if contribution pursuant to this Section 7 were determined by pro rata allocation or by any other method of allocation that does not take account of the equitable considerations referred to in Section ‎7(d). The amount paid or payable by an indemnified party as a result of the losses, claims, damages and liabilities referred to in Section ‎7(d) shall be deemed to include, subject to the limitations set forth above, any legal or other expenses reasonably incurred and documented by such indemnified party in connection with investigating or defending any such action or claim. Notwithstanding the provisions of this Section ‎7, the Underwriters shall not be required to contribute any amount in excess of the amount by which the total price at which the Shares sold by them were offered to the public exceeds the amount of any damages that the Underwriters has otherwise been required to pay by reason of such untrue or alleged untrue statement or omission or alleged omission. No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of the Securities Act) shall be entitled to contribution from any person who was not guilty of such fraudulent misrepresentation. The remedies provided for in this Section ‎7 are not exclusive and shall not limit any rights or remedies which may otherwise be available to any indemnified party at law or in equity.

(f)The indemnity and contribution provisions contained in this Section 7 and the representations, warranties and other statements of the Company contained in this Agreement shall remain operative and in full force and effect regardless of any termination of this Agreement, any investigation made by or on behalf of the Underwriters, any person controlling the Underwriters or any affiliate of the Underwriters or by or on behalf of the Company, its officers or directors or any person controlling the Company and acceptance of and payment for any of the Shares.

8.Effectiveness. This Agreement shall become effective upon the execution and delivery hereof by the parties hereto.

9.Defaulting Underwriters. If, on the Closing Date or an Option Closing Date, as the case may be, any one or more of the Underwriters shall fail or refuse to purchase Shares that it has or they have agreed to purchase hereunder on such date, and the aggregate number of Shares which such defaulting Underwriter or Underwriters agreed but failed or refused to purchase is not more than one-tenth of the aggregate number of the Shares to be purchased on such

date, the other Underwriters shall be obligated severally in the proportions that the number of Firm Shares set forth opposite their respective names in Schedule I bears to the aggregate number of Firm Shares set forth opposite the names of all such non-defaulting Underwriters, or in such other proportions as the Representatives may specify, to purchase the Shares which such defaulting Underwriter or Underwriters agreed but failed or refused to purchase on such date; provided that in no event shall the number of Shares that any Underwriter has agreed to purchase pursuant to this Agreement be increased pursuant to this Section 9 by an amount in excess of one-ninth of such number of Shares without the written consent of such Underwriter. If, on the Closing Date, any Underwriter or Underwriters shall fail or refuse to purchase Firm Shares and the aggregate number of Firm Shares with respect to which such default occurs is more than one-tenth of the aggregate number of Firm Shares to be purchased on such date, and arrangements satisfactory to the Representatives and the Company for the purchase of such Firm Shares are not made within 36 hours after such default, this Agreement shall terminate without liability on the part of any non-defaulting Underwriter or the Company. In any such case either the Representatives or the Company shall have the right to postpone the Closing Date, but in no event for longer than seven days, in order that the required changes, if any, in the Registration Statement, in the Time of Sale Prospectus, in the Prospectus or in any other documents or arrangements may be effected. If, on an Option Closing Date, any Underwriter or Underwriters shall fail or refuse to purchase Additional Shares and the aggregate number of Additional Shares with respect to which such default occurs is more than one-tenth of the aggregate number of Additional Shares to be purchased on such Option Closing Date, the non-defaulting Underwriters shall have the option to (i) terminate their obligation hereunder to purchase the Additional Shares to be sold on such Option Closing Date or (ii) purchase not less than the number of Additional Shares that such non-defaulting Underwriters would have been obligated to purchase in the absence of such default. Any action taken under this paragraph shall not relieve any defaulting Underwriter from liability in respect of any default of such Underwriter under this Agreement.

10.Termination. The Underwriters, or any of them, may terminate this Agreement by notice to the Company, if after the execution and delivery of this Agreement and prior to or on the Closing Date, (i) trading generally shall have been suspended or materially limited on, or by, as the case may be, any of the NYSE, the NYSE American, or the NASDAQ Global Market, (ii) trading of any securities of the Company shall have been suspended on the NYSE, (iii) a material disruption in securities settlement, payment or clearance services in the United States shall have occurred, (iv) any moratorium on commercial banking activities shall have been declared by Federal, New York State, or Swiss authorities or (v) there shall have occurred any outbreak or escalation of hostilities, or any change in financial markets or any calamity or crisis that, in the Underwriters’ reasonable judgment, is material and adverse and which, singly or

together with any other event specified in this clause (v), makes it, in the Underwriter’s reasonable judgment, impracticable or inadvisable to proceed with the offer, sale or delivery of the Shares on the terms and in the manner contemplated in the Time of Sale Prospectus or the Prospectus.

11.Entire Agreement.

(a)This Agreement represents the entire agreement between the Company and the Underwriters with respect to the preparation of the Preliminary Prospectus, the Time of Sale Prospectus or the Prospectus, the conduct of the offering and the issuance and sale of the Shares.

(b)The Company acknowledges that in connection with the offering of the Shares: (i) the Underwriters have acted and will act at arm’s length and owe no fiduciary duties to, the Company or any other person, (ii) the Underwriters owe the Company only those duties and obligations set forth in this Agreement, any contemporaneous written agreement and prior written agreements (to the extent not superseded by this Agreement), if any, (iii) the Underwriters may have interests that differ from those of the Company, and (iv) none of the activities of the Underwriters in connection with the transactions contemplated herein constitutes a recommendation, investment advice, or solicitation of any action by the Underwriters with respect to any entity or natural person. The Company waives to the full extent permitted by applicable law any claims it may have against the Underwriters arising from an alleged breach of fiduciary duty in connection with the sale and distribution of the Shares.

12.Recognition of the U.S. Special Resolution Regimes.

(a)In the event that the any of the Underwriters is a Covered Entity that becomes subject to a proceeding under a U.S. Special Resolution Regime, the transfer from each of the Underwriters of this Agreement, and any interest and obligation in or under this Agreement, will be effective to the same extent as the transfer would be effective under the U.S. Special Resolution Regime if this Agreement, and any such interest and obligation, were governed by the laws of the United States or a state of the United States.

(b)In the event that any of the Underwriters is a Covered Entity or a BHC Act Affiliate of any of the Underwriters becomes subject to a proceeding under a U.S. Special Resolution Regime, Default Rights under this Agreement that may be exercised against the Underwriters are permitted to be exercised to no greater extent than such Default Rights could be exercised under the U.S. Special Resolution Regime if this Agreement were governed by the laws of the United States or a state of the United States.

For purposes of this Section 12, a “BHC Act Affiliate” has the meaning assigned to the term “affiliate” in, and shall be interpreted in accordance with, 12 U.S.C. § 1841(k).

“Covered Entity” means any of the following: (i) a “covered entity” as that term is defined in, and interpreted in accordance with, 12 C.F.R. § 252.82(b); (ii) a “covered bank” as that term is defined in, and interpreted in accordance with, 12 C.F.R. § 47.3(b); or (iii) a “covered FSI” as that term is defined in, and interpreted in accordance with, 12 C.F.R. § 382.2(b). “Default Right” has the meaning assigned to that term in, and shall be interpreted in accordance with, 12 C.F.R. §§ 252.81, 47.2 or 382.1, as applicable. “U.S. Special Resolution Regime” means each of (i) the Federal Deposit Insurance Act and the regulations promulgated thereunder and (ii) Title II of the Dodd-Frank Wall Street Reform and Consumer Protection Act and the regulations promulgated thereunder.

13.Counterparts. This Agreement may be signed by manual or other electronic (including “.pdf”) signature in two or more counterparts, each of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument.

14.Applicable Law. This Agreement and any claim, controversy or dispute arising under or related thereto shall be governed by and construed in accordance with the internal laws of the State of New York.

15.Headings. The headings of the sections of this Agreement have been inserted for convenience of reference only and shall not be deemed a part of this Agreement.

16.Notices. All communications hereunder shall be in writing and effective only upon receipt and if to the Representatives shall be delivered, mailed or sent to Citigroup Global Markets Inc., 388 Greenwich Street, New York, New York 10013 Attention: General Counsel, facsimile number 1-646-291-1469, or to Morgan Stanley & Co. LLC, 1585 Broadway, New York, New York 10036, Attention: Equity Syndicate Desk, with a copy to the Legal Department; and if to the Company shall be delivered, mailed or sent to Turmstrasse 30, 6312 Steinhausen, Switzerland (Attn: Corporate Secretary) or to Sandro.Thoma@deepwater.com.

17.Submission to Jurisdiction; Appointment of Agents for Service.

(a)The Company irrevocably submits to the non-exclusive jurisdiction of any New York State or United States Federal court sitting in The City of New York (the “Specified Courts”) over any suit, action or proceeding arising out of or relating to this Agreement, the Prospectus, the Registration Statement or the offering of the Shares (each, a “Related Proceeding”). The Company irrevocably waives, to the fullest extent permitted by law, any objection which it may now or hereafter have to the laying of venue of any Related Proceeding brought in such a court and any claim that any such Related Proceeding brought in such a court has been brought in an inconvenient forum. To the extent that the Company has or hereafter may acquire any immunity (on the grounds of sovereignty or otherwise) from the jurisdiction of any court or

from any legal process with respect to itself or its property, the Company irrevocably waives, to the fullest extent permitted by law, such immunity in respect of any such suit, action or proceeding.

(b)The Company hereby irrevocably appoints Transocean Offshore Deepwater Drilling Inc., with offices at 1414 Enclave Parkway, Houston, Texas 77077, as its agent for service of process in any Related Proceeding and agrees that service of process in any such Related Proceeding may be made upon it at the office of such agent. The Company waives, to the fullest extent permitted by law, any other requirements of or objections to personal jurisdiction with respect thereto. The Company represents and warrants that such agent has agreed to act as the Company’s agent for service of process, and the Company agrees to take any and all action, including the filing of any and all documents and instruments, that may be necessary to continue such appointment in full force and effect.

18.Judgment Currency. If for the purposes of obtaining judgment in any court it is necessary to convert a sum due hereunder into any currency other than United States dollars, the parties hereto agree, to the fullest extent permitted by law, that the rate of exchange used shall be the rate at which in accordance with normal banking procedures the Underwriters could purchase United States dollars with such other currency in The City of New York on the business day preceding that on which final judgment is given. The obligation of the Company with respect to any sum due from it to the Underwriters or any person controlling the Underwriters shall, notwithstanding any judgment in a currency other than United States dollars, not be discharged until the first business day following receipt by the Underwriters or controlling person of any sum in such other currency, and only to the extent that the Underwriters or controlling person may in accordance with normal banking procedures purchase United States dollars with such other currency. If the United States dollars so purchased are less than the sum originally due to the Underwriters or controlling person hereunder, the Company agrees as a separate obligation and notwithstanding any such judgment, to indemnify the Underwriters or controlling person against such loss. If the United States dollars so purchased are greater than the sum originally due to the Underwriters or controlling person hereunder, the Underwriters or controlling person agrees to pay to the Company an amount equal to the excess of the dollars so purchased over the sum originally due to the Underwriters or controlling person hereunder.

[Signature page follows]


Very truly yours, TRANSOCEAN LTD.
By:	/s/ Sandro Thoma
	Name: Sandro Thoma
	Title: Corporate Secretary


Accepted as of the date first written above Citigroup Global Markets Inc.
By:	/s/ Ben Exner
	Name: Ben Exner
	Title: Managing Director


Morgan Stanley & Co. LLC
By:	/s/ Daniel J. F. McCullough
	Name: Daniel J. F. McCullough
	Title: Executive Director

[Signature Page to the Underwriting Agreement]

SCHEDULE I

Underwriter	Number of Shares To Be Purchased
Citigroup Global Markets Inc.	48,828,125
Morgan Stanley & Co. LLC	48,828,125
DNB Markets, Inc.	8,203,125
Goldman Sachs & Co. LLC	7,656,250
Wells Fargo Securities, LLC	7,656,250
SB1 Markets AS	2,734,375
The Standard Bank of South Africa Limited	1,093,750

Total:‌	125,000,000

I-1

SCHEDULE II

Time of Sale Prospectus

1)	Preliminary Prospectus dated September 24, 2025

2)	Pricing Information:

Number of Firm Shares: 125,000,000

Number of Option Shares: 18,750,000

Purchase price per Share: $2.93

Price to public per Share: $3.05

Settlement Date: September 26, 2025 (T+1)

II-1