Exhibit 99.1

Stratus Stockholders Support Stratus Board and Management at Annual

Meeting and Reject Carl Berg’s Nominees and Proposal

AUSTIN, TX, June 6, 2016 — Stratus Properties Inc. (NASDAQ: STRS) (the “Company” or “Stratus”) is pleased to announce that, based on the preliminary vote count provided by our proxy solicitor, stockholders voted to reelect Stratus’ director nominees — Messrs. William “Beau” Armstrong and Charles Porter — to the Stratus Board of Directors and to reject the stockholder proposal presented by Carl E. Berg. The Company held its annual meeting of stockholders earlier today.

William H. Armstrong III, Chairman of the Board, President and Chief Executive Officer of Stratus, stated: “We are pleased with the outcome of today’s vote and are committed to continuing to work to maximize long-term value for all stockholders by building value in our remarkable portfolio of properties in the growing Austin market and completing our review of strategic alternatives. We appreciate the feedback we received from our stockholders, and our Board intends to continue to be responsive to stockholder input that it believes would benefit all stockholders. On behalf of Stratus Properties’ entire Board and management team, we wish to thank our stockholders for their continued support.”

Preliminary results also indicate that, in addition to reelecting Messrs. Armstrong and Porter to Stratus’ Board, Stratus’ stockholders:

As previously announced, the Stratus Board has engaged a nationally recognized investment banking firm, Hentschel & Company, to explore all strategic alternatives.

Stratus will file final voting results with the SEC on Form 8-K once they are certified by the independent inspector of elections.

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, the report of the inspector of elections certifying the final results of the votes at the annual meeting of stockholders, the outcome of the strategic review process, 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 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, filed with the SEC.

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.

2

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.

About Stratus Properties Inc.

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, Texas area, but including projects in certain other select markets in Texas.

3