Exhibit 5.1

October 5, 2022

Reata Pharmaceuticals, Inc.

5320 Legacy Drive

Plano, Texas 75024

Ladies and Gentlemen:

We have acted as counsel for Reata Pharmaceuticals, Inc., a Delaware corporation (the “Company”), in connection with the Company’s registration under the Securities Act of 1933, as amended (the “Act”), of the offer and sale of an aggregate of up to 500,000 shares of the Company’s Class A common stock, par value $0.001 per share (the “Stock”), which shares may be issued from time to time in accordance with the terms of the Reata Pharmaceuticals, Inc. 2022 Employee Stock Purchase Plan (as amended from time to time, the “Plan”), pursuant to the Company’s registration statement on Form S-8 (the “Registration Statement”) to be filed with the Securities and Exchange Commission on October 5, 2022.

In reaching the opinions set forth herein, we have examined and are familiar with originals or copies, certified or otherwise identified to our satisfaction, of such documents and records of the Company and such statutes, regulations and other instruments as we deemed necessary or advisable for purposes of this opinion, including (i) the Registration Statement, (ii) certain resolutions adopted by the board of directors of the Company, (iii) the Plan, and (iv) such other certificates, instruments, and documents as we have considered necessary for purposes of this opinion. As to any facts material to our opinions, we have made no independent investigation or verification of such facts and have relied, to the extent that we deem such reliance proper, upon certificates of public officials and officers or other representatives of the Company.

We have assumed (i) the legal capacity of all natural persons, (ii) the genuineness of all signatures, (iii) the authority of all persons signing all documents submitted to us on behalf of the parties to such documents, (iv) the authenticity of all documents submitted to us as originals, (v) the conformity to authentic original documents of all documents submitted to us as copies, (vi) that all information contained in all documents reviewed by us is true, correct and complete, and (vii) that the shares of Stock will be issued in accordance with the terms of the Plan or other governing documentation.

Based on the foregoing and subject to the limitations set forth herein, and having due regard for the legal considerations we deem relevant, we are of the opinion that the shares of Stock have been duly authorized and, when the shares of Stock are issued by the Company in accordance with the terms of the Plan or other governing documentation and the instruments executed pursuant to the Plan or other governing documentation, as applicable, the shares of Stock will be validly issued, fully paid and non-assessable.

This opinion is limited in all respects to the General Corporation Law of the State of Delaware. We express no opinion as to any other law or any matter other than as expressly set forth above, and no opinion as to any other law or matter may be inferred or implied herefrom. The opinions expressed herein are rendered as of the date hereof and we expressly disclaim any obligation to update this letter or advise you of any change in any matter after the date hereof.

This opinion may be filed as an exhibit to the Registration Statement. In giving this consent, we do not thereby admit that we come within the category of persons whose consent is required under Section 7 of the Act.

Very truly yours,

/s/ Vinson & Elkins L.L.P.