Exhibit 99.1

FOR IMMEDIATE RELEASE

INVESTOR CONTACT

Julie Anderson, 214.932.6773

julie.anderson@texascapitalbank.com

MEDIA CONTACT

Shannon Wherry, 469.399.8527

shannon.wherry@texascapitalbank.com

Texas Capital Bancshares, Inc. Announces Executive Leadership Change

C. Keith Cargill Steps Down as President and Chief Executive Officer

Larry L. Helm to Serve as Executive Chair, CEO and President Until a Permanent Successor Is Named

DALLAS - May 26, 2020 - Texas Capital Bank, N.A., and its parent company Texas Capital Bancshares, Inc. (NASDAQ: TCBI), collectively referred to herein as “Texas Capital,” today announced that C. Keith Cargill has stepped down as President and Chief Executive Officer and a member of the Board of Directors of both companies, effective immediately. Larry L. Helm, who has served as Chairman of the Texas Capital Bancshares Board since 2012, will serve as Executive Chair, CEO and President of both companies until a permanent successor has been named. Mr. Cargill will serve as Vice Chairman of both companies through the end of 2020 to help support a smooth transition. In addition, James H. Browning, an independent director and member of the Texas Capital Bancshares Board since 2009, has been appointed Lead Director.

Texas Capital Bancshares’ Board intends to conduct a search process to identify a permanent CEO and continues to be engaged with Egon Zehnder, a leading executive search firm, as part of the Board’s robust and ongoing succession planning process.

Mr. Helm has served as a director of the Texas Capital Bancshares Board since 2006, contributing significant operational and financial expertise. He has extensive knowledge of Texas Capital’s strategy, operations and culture having worked closely with the Texas Capital management team. During his tenure, Mr. Helm has provided important oversight and counsel to support Texas Capital in driving shareholder value and growth as well as navigating challenging market environments. He brings more than 30 years of commercial banking experience, including management positions at Bank One Corporation, most notably as CEO Dallas Region and CEO U.S. Middle Market Banking. In addition, he brings substantial executive-level experience with publicly-traded companies, including Halcón Resources Corporation and Petrohawk Energy Corporation.

Elysia Ragusa, Chair of the Texas Capital Bancshares Governance and Nominating Committee, said, “As part of our focus on succession planning, the Board believes that it is the right time for a transition in leadership as the Company executes a strategy to achieve enhanced operational focus and profitable, long-term value creation. We are fortunate to have someone of Larry’s caliber and experience ready to assume the role of Executive Chair, CEO and President at this important juncture for the Company. Larry has worked closely with the entire management team over the last 14 years, gaining a deep understanding of the Company’s unique opportunities. We are confident that he is the right person to lead Texas Capital Bank until we have identified a permanent successor for the CEO role.”

Mr. Cargill said, “After much deliberation, the Board and I have decided that now is the right time for me to step down as President and CEO of Texas Capital Bancshares and Texas Capital Bank. It has been one of the greatest honors of my life to be one of the founders of this great company and serve as CEO alongside our exceptional management team and our talented colleagues. Our team has transformed Texas Capital Bank into one the most successful banks in the country that caters to entrepreneurs, business owners, private wealth clients and other loyal individuals.”

Mr. Helm said, “Under Keith’s leadership, the Texas Capital Bank team has built one of the best, fastest-growing business and private wealth banks in the United States. Through multiple cycles, the Company has achieved significant growth by fostering top talent and a culture of integrity, innovation and collaboration, earning and keeping the trust of our clients through exceptional service and meeting the needs of middle-market entrepreneurs. With this strong foundation in place, the team is well positioned to continue executing against the Company’s strategic priorities and generate returns for our clients and shareholders.”

“On behalf of the entire Board, I want to thank Keith for his contributions as CEO and as a founder of Texas Capital Bank,” said Mr. Helm. “I look forward to working with Keith and our leadership team to ensure a smooth transition for all our stakeholders,

particularly as we navigate the current impact presented by the global pandemic. We wish Keith the very best in his future endeavors.”

About Larry L. Helm

Larry Helm has served as Chairman of the Texas Capital Bancshares Board of Directors since 2012 and as a director since 2006. He currently serves as a Senior Advisor to Accelerate Resources, a company engaged in the development and production of oil and gas assets. From January 2013 to April 2016, he was Executive Vice President of Corporate Affairs for Halcón Resources Corporation, a company engaged in the exploration, development and production of oil and gas. Prior to Halcón Resources, Mr. Helm served as Chief Administrative Officer of Petrohawk Energy Corporation from 2004 until its sale to BHP Billiton in 2011. Mr. Helm served as Vice President Transition with BHP Billiton until his employment with Halcón Resources.

From January 1973 to January 2004, Mr. Helm was engaged in the commercial banking business including executive management positions with Bank One Corporation and others, most notably as CEO Dallas Region and CEO U.S. Middle Market Banking. Mr. Helm has substantial experience in middle market and energy lending.

Mr. Helm received an MBA in Banking and Finance from the University of North Texas and a BS in Business Administration from Trinity University in San Antonio, Texas.

About Texas Capital Bancshares, Inc.

Texas Capital Bancshares, Inc. (NASDAQ: TCBI), a member of the Russell 1000^® Index and the S&P MidCap 400^®, is the parent company of Texas Capital Bank, N.A., a commercial bank that delivers highly personalized financial services to businesses and entrepreneurs. Headquartered in Dallas, the bank has full-service locations in Austin, Dallas, Fort Worth, Houston and San Antonio.

Forward Looking Statements

This communication may be deemed to include “forward-looking statements” within the meaning of the Private Securities Litigation Reform Act of 1995 regarding the financial condition, results of operations, business plans and the future performance of Texas Capital Bancshares, Inc. (“TCBI”). These statements are not historical in nature and can generally be identified by such words as “believe,” “expect,” “estimate,” “anticipate,” “plan,” “may,” “will,” “forecast,” “could,” “projects,” “intend” and similar expressions. Because forward-looking statements relate to future results and occurrences, they are subject to inherent uncertainties, risks, and changes in circumstances that are difficult to predict. A number of factors, many of which are beyond our control, could cause actual results to differ materially from future results expressed or implied by such forward-looking statements. These risks and uncertainties include, but are not limited to, the credit quality of our loan portfolio, general economic conditions in the United States and in our markets, including the continued impact on our customers from volatility in oil and gas prices, the material risks and uncertainties for the U.S. and world economies, and for our business, resulting from the COVID-19 pandemic, expectations regarding rates of default and loan losses, volatility in the mortgage industry, our business strategies, and our expectations about future financial performance, future growth and earnings, the appropriateness of our allowance for loan losses and provision for credit losses, the impact of changing regulatory requirements and legislative changes on our business, increased competition, interest rate risk, new lines of business, new product or service offerings and new technologies. These and other factors that could cause results to differ materially from those described in the forward-looking statements, as well as a discussion of the risks and uncertainties that may affect our business, can be found in our Annual Report on Form 10-K, our Quarterly Reports on Form 10-Q and in other filings we make with the Securities and Exchange Commission. The information contained in this communication speaks only as of its date. Except to the extent required by applicable law or regulation, TCBI disclaims any obligation to update such factors or to publicly announce the results of any revisions to any of the forward-looking statements included herein to reflect future events or developments.