Reata Pharmaceuticals (RETA) 8-K Entry into a Material Definitive Agreement

Exhibit 5.1

November 14, 2019

Reata Pharmaceuticals, Inc.

5320 Legacy Drive

Plano, Texas 75024

Ladies and Gentlemen:

We have acted as counsel to Reata Pharmaceuticals, Inc., a Delaware corporation (the “Company”), with respect to certain legal matters in connection with the offer and sale (the “Offering”) by the Company of 2,400,000 shares (the “Firm Securities”) of the Company’s Class A common stock, par value $0.001 per share (the “Class A Common Stock”), and up to an additional 360,000 shares (the “Option Securities,” and together with the Firm Securities, the “Securities”) of Class A Common Stock, each of which are being sold pursuant to the Underwriting Agreement dated as of November 13, 2019 (the “Underwriting Agreement”), between the Company and Citigroup Global Markets Inc., Jefferies LLC and SVB Leerink LLC, as representatives of the several Underwriters named in Schedule III attached thereto (the “Underwriters”); the Securities have been offered for sale pursuant to a prospectus supplement dated November 13, 2019 (the “Prospectus Supplement”), filed with the Securities and Exchange Commission (the “Commission”) pursuant to Rule 424(b) on November 14, 2019, to a prospectus dated July 23, 2018 (as amended and supplemented by the Prospectus Supplement, the “Prospectus”) that constitutes a part of the Company’s automatically effective Registration Statement on FormS-3 (RegistrationNo. 333-226289), filed with the Commission on July 23, 2018 (the “Registration Statement”).

We have examined (i) the Underwriting Agreement; (ii) the Registration Statement; (iii) the Prospectus Supplement; (iv) the Prospectus; (v) the Thirteenth Amended and Restated Certificate of Incorporation of the Company and the Second Amended and Restated Bylaws of the Company; (vi) resolutions adopted by the Board of Directors of the Company relating to the Registration Statement, the Offering and related matters; (vii) resolutions adopted by the Pricing Committee of the Board of Directors of the Company relating to the Offering; and (viii) such other certificates, statutes and other instruments and documents as we considered appropriate for purposes of the opinions hereafter expressed. In addition, we reviewed such questions of law as we considered appropriate.

As to any facts material to the opinions contained herein, we have made no independent investigation 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.

Vinson & Elkins LLP Attorneys at Law Austin Beijing Dallas Dubai Hong Kong Houston London New York Richmond Riyadh San Francisco Tokyo Washington Trammell Crow Center, 2001 Ross Avenue, Suite 3900 Dallas, TX 75201-2975 Tel +1.214.220.7700Fax +1.214.220.7716 www.velaw.com

November 14, 2019 Page 2

In connection with rendering the opinion set forth below, we have assumed that (i) all information contained in all documents reviewed by us is true and correct; (ii) all signatures on all documents examined by us are genuine; (iii) all documents submitted to us as originals are authentic and complete; (iv) all documents submitted to us as copies conform to the originals of those documents; (v) all persons executing and delivering the documents we examined were competent to execute and deliver such documents; (vi) all Securities will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and Prospectus; and (vii) the Underwriting Agreement has been duly authorized and validly executed and delivered by the Underwriters and constitutes a legal, valid and binding obligation of the Underwriters, and the Underwriters have the requisite organizational and legal power and authority to perform their obligations under the Underwriting Agreement.

Based on the foregoing, and subject to the assumptions, qualifications, limitations and exceptions set forth herein, we are of the opinion that the Securities to be issued and sold by the Company to the Underwriters as contemplated by the Underwriting Agreement have been duly authorized and, upon payment and delivery in accordance with the Underwriting Agreement, will be validly issued, fully paid andnon-assessable.

The foregoing opinions are limited in all respects to the Delaware General Corporation Law (including the applicable provisions of the Delaware Constitution and the reported judicial decisions interpreting these laws) and the federal laws of the United States of America as in effect on the date hereof, and we undertake no duty to update or supplement the foregoing opinions to reflect any facts or circumstances that may hereafter come to our attention or to reflect any changes in any law that may hereafter occur or become effective. We express no opinion as to the effect of the laws of any other jurisdiction, domestic or foreign, or to any matter other than as expressly set forth above, and no opinion on any other matter may be inferred or implied herefrom.

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We hereby consent to the filing of this opinion as an exhibit to the Current Report on Form8-K dated on or about the date hereof, and to the use of our name in the Prospectus forming a part of the Registration Statement under the caption “Legal Matters.” By giving such consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Vinson & Elkins L.L.P.