Exhibit 99.1

Stratus Properties Inc. Announces

Appointment of John C. Schweitzer to its Board of Directors

AUSTIN, TX, March 28, 2016—Stratus Properties Inc. (NASDAQ: STRS) announced today the appointment of John C. Schweitzer to its Board of Directors. Mr. Schweitzer was appointed by the Board upon the recommendation of the Nominating and Corporate Governance Committee, will serve as a Class II director and will be up for re-election to the Board in 2018. He will fill a vacancy created by the resignation of John G. Wenker.

John C. Schweitzer, age 71, has over 40 years of experience in the real estate industry and has previously served on the boards of numerous public companies. He has a strong background in business and finance with extensive experience in public company strategies, executive compensation and human resources. Mr. Schweitzer has served as President of Westgate Corporation, a real estate investment and venture capital firm headquartered in Austin, Texas, since 1977. He also currently serves as lead director of Regency Centers Corporation, a publicly-traded real estate investment trust, and has served on its Board since 1999. Mr. Schweitzer previously served as a member of Pacific Retail Trust’s Board of Trustees before its merger into Regency in 1999 and as a director or officer of a number of other public companies and financial institutions, including Archstone-Smith Trust, J.P. Morgan Chase Bank of Texas-Austin, Franklin Federal Bancorp, Elgin Clock Company, El Paso Electric Company, MBank El Paso, the Circle K Corporation, Homestead Village Incorporated and Enerserv Products.

William H. Armstrong III, Chairman of the Board, President and Chief Executive Officer of Stratus, stated, “We are pleased to welcome John Schweitzer to our Board of Directors and look forward to his guidance and counsel. John’s extensive experience as a Board member and in-depth knowledge of the Austin real estate market will make him a valuable member of our Board of Directors. His strong background in business and finance will allow him to provide strategic insight as we implement our Board-approved five-year plan.”

Stratus’ Board of Directors is comprised of six members, including five independent directors, who possess a diverse range of perspectives and experience.

Stratus is a diversified real estate company engaged primarily in the acquisition, entitlement, development, management, operation and sale of commercial, hotel, entertainment, and multi- and single-family residential real estate properties, primarily located in the Austin area, but including projects in certain other select markets in Texas.

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A copy of this release is available on Stratus’ website, www.stratusproperties.com.

Important Additional Information

Stratus Properties Inc., its directors and certain of its executive officers may be deemed to be participants in the solicitation of proxies from Stratus stockholders in connection with the matters to be considered at Stratus’ 2016 annual meeting of stockholders. Stratus intends to file a proxy statement and white proxy card with the U.S. Securities and Exchange Commission (the “SEC”) in connection with any such solicitation of proxies from Stratus stockholders. STRATUS STOCKHOLDERS ARE STRONGLY ENCOURAGED TO READ ANY SUCH PROXY STATEMENT AND ACCOMPANYING WHITE PROXY CARD WHEN THEY BECOME AVAILABLE AS THEY WILL CONTAIN IMPORTANT INFORMATION. Information regarding the ownership of Stratus’ directors and executive officers in Stratus stock, restricted stock units and stock options is included in their SEC filings on Forms 3, 4, and 5, which can be found through Stratus’ website (www.stratusproperties.com) under “Investor Relations—SEC Filings” or through the SEC’s website at www.sec.gov. Information can also be found in Stratus’ other SEC filings, including Stratus’ definitive proxy statement for the 2015 annual meeting of stockholders and its Annual Report on Form 10-K for the year ended December 31, 2015. More detailed and updated information regarding the identity of potential participants, and their direct or indirect interests, by security holdings or otherwise, will be set forth in the proxy statement and other materials to be filed with the SEC in connection with Stratus’ 2016 annual meeting of stockholders. Stockholders will be able to obtain any proxy statement, any amendments or supplements to the proxy statement and other documents filed by Stratus with the SEC for no charge at the SEC’s website at www.sec.gov. Copies will also be available at no charge at Stratus’ website at www.stratusproperties.com, by writing to Stratus Properties Inc. at 212 Lavaca Street, Suite 300, Austin, TX 78701, or by calling Stratus’ proxy solicitor, Innisfree M&A Incorporated, toll-free at 888-750-5834.

Cautionary Statement Regarding Forward-Looking Statements

This press release contains forward-looking statements in which Stratus discusses factors it believes may affect its future performance. Forward-looking statements are all statements other than statements of historical facts, such as statements regarding the implementation and potential results of Stratus’ five-year plan, projections or expectations related to operational and financial performance or liquidity, reimbursements for infrastructure costs, financing and regulatory matters, development plans and sales of properties, commercial leasing activities, timeframes for development, construction and completion of Stratus’ projects, capital expenditures, liquidity and capital resources, and other plans and objectives of management for future operations and activities. The words “anticipates,” “may,” “can,” “plans,” “believes,” “potential,” “estimates,” “expects,” “projects,” “intends,” “likely,” “will,” “should,” “to be” and any similar expressions and/or statements that are not historical facts are intended to identify those assertions as forward-looking statements.

Stratus cautions readers that forward-looking statements are not guarantees of future performance, and its actual results may differ materially from those anticipated, projected or assumed in the forward-looking statements. Important factors that can cause Stratus’ actual results to differ materially from those anticipated in the forward-looking statements include, but are not limited to, Stratus’ ability to refinance and service its debt and the availability of financing for development projects and other corporate purposes, Stratus’ ability to sell properties at prices its board considers acceptable, a decrease

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in the demand for real estate in the Austin, Texas market, changes in economic and business conditions, reductions in discretionary spending by consumers and corporations, competition from other real estate developers, hotel operators and/or entertainment venue operators and promoters, business opportunities that may be presented to and/or pursued by Stratus, the termination of sales contracts or letters of intent due to, among other factors, the failure of one or more closing conditions or market changes, the failure to attract customers for its developments or such customers’ failure to satisfy their purchase commitments, increases in interest rates, declines in the market value of its assets, increases in operating costs, including real estate taxes and the cost of construction materials, changes in external perception of the W Austin Hotel, changes in consumer preferences, changes in laws, regulations or the regulatory environment affecting the development of real estate, opposition from special interest groups with respect to development projects, weather-related risks and other factors described in more detail under the heading “Risk Factors” in Stratus’ Annual Report on Form 10-K for the year ended December 31, 2015.

Investors are cautioned that many of the assumptions upon which Stratus’ forward-looking statements are based are likely to change after the forward-looking statements are made. Further, Stratus may make changes to its business plans that could affect its results. Stratus cautions investors that it does not intend to update its forward-looking statements notwithstanding any changes in its assumptions, business plans, actual experience, or other changes, and Stratus undertakes no obligation to update any forward-looking statements.

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