Exhibit 5.1

September 21, 2012

Texas Capital Bancshares, Inc.

2000 McKinney Avenue, Suite 700

Dallas, Texas 75201

Ladies and Gentlemen:

We have acted as legal counsel to Texas Capital Bancshares, Inc. (the “Company”) in connection with the public offering of $111,000,000 of Subordinated Notes due 2042 of the Company (the “Notes”) to be offered and sold by the Company pursuant to (i) a preliminary prospectus supplement dated September 17, 2012, and (ii) a final prospectus supplement dated September 18, 2012 and the accompanying prospectus dated July 16, 2012 (such documents, collectively, the “Prospectus”) that form part of the Company’s effective registration statement on Form S-3, as amended (File No. 333-181471) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission under the Securities Act of 1933, as amended.

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act of 1933, as amended (the “Securities Act”).

In connection with this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of (i) the Registration Statement, (ii) the Prospectus, (iii) the form of Note, (iv) the Certificate of Incorporation, as amended, of the Company, as currently in effect, (v) the Bylaws, as amended, of the Company, as currently in effect, and (vi) certain resolutions adopted by the Board of Directors, or a committee thereof, of the Company with respect to the issuance of the Notes. We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates of public officials, certificates of officers or other representatives of the Company and others, and such other documents, certificates and records, as we have deemed necessary or appropriate as a basis for the opinion set forth herein.

In our examination, we have assumed and have not verified (i) the legal capacity of all natural persons, (ii) the genuineness of all signatures (other than persons signing on behalf of the Company), (iii) the authenticity of all documents submitted to us as originals, (iv) the conformity with the originals of all documents supplied to us as copies, (v) the accuracy and completeness of all corporate records and documents made available to us by the Company, and (vi) that the foregoing documents, in the form submitted to us for our review, have not been altered or amended in any respect material to our opinion stated herein. We have relied as to factual matters upon certificates from officers of the Company and certificates and other documents from public officials and government agencies and departments and we have assumed the accuracy and authenticity of such certificates and documents. We have further assumed that the Notes were issued and delivered in accordance with the terms of the Underwriting Agreement, dated September 18, 2012, among the Company, Deutsche Bank Securities Inc., Macquarie Capital (USA) Inc., and U.S. Bancorp Investments, Inc. and the other underwriters identified therein.

The following opinion is limited in all respects to matters of the General Corporation Law of the State of Delaware (including the statutory provisions, all applicable provisions of the Delaware Constitution and reported judicial decisions interpreting the foregoing), the laws of the State of New York and U.S. federal law, and we express no opinion as to the laws of any other jurisdiction.

Based on the foregoing, and subject to the assumptions, qualifications and limitations set forth herein, as of the date hereof, we are of the opinion that the Notes have been duly authorized, executed and delivered by the Company and (assuming the due authorization, execution and delivery thereof by the Trustee) constitute binding obligations of the Company, except as may be limited by bankruptcy, insolvency (including, without limitation, all laws relating to fraudulent transfers), reorganization, moratorium or similar laws affecting enforcement of creditors’ rights generally and subject to general principles of equity.

Texas Capital Bancshares, Inc.

September 21, 2012

Page 2

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement. We also consent to the reference to our firm under the caption “Legal Matters” in the Prospectus. In giving this consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.