Exhibit 99.1

STRATUS PROPERTIES INC. ADOPTS

SHAREHOLDER RIGHTS PLAN TO PROTECT SHAREHOLDER INTERESTS

DURING REIT EXPLORATION

AUSTIN, TX, September 22, 2020 - Stratus Properties Inc. (NASDAQ: STRS) (“Stratus” or the “Company”) announced today that its Board of Directors (the “Board”) has unanimously adopted a limited-duration shareholder rights plan (the “Rights Plan”) to ensure shareholders have the benefit of the previously announced exploration of a potential conversion to a real estate investment trust (“REIT”).

The Rights Plan is intended to reduce the likelihood that concentrated share ownership adversely impacts the Company’s ability to qualify as and be taxed as a REIT. In order to qualify as a REIT, among other requirements, not more than 50% of a company’s shares may be beneficially owned by five or fewer individuals.

The Rights Plan is effective immediately, and the record date for the Rights distribution is October 2, 2020. The Rights will expire on September 22, 2023. However, the Rights will expire prior to that date at the earlier of (i) the time at which the Company’s conversion to a REIT becomes effective and (ii) the close of business on December 31, 2021 unless shareholder approval has been obtained on or prior to such date.

The Rights Plan is similar to other rights plans adopted by publicly-held companies. The Rights will be exercisable only if a person or group acquires beneficial ownership (including certain derivatives) of 9.8% or more of the outstanding common stock of Stratus. Any shareholders with beneficial ownership of 9.8% or more of the outstanding common stock of Stratus as of the time of this announcement are grandfathered at their current ownership levels (i.e., they are not required to sell but are not permitted to increase their ownership without triggering the Rights).

Shareholders are not required to take any action to receive the distribution of their Rights.

Additional information regarding the Rights Plan will be contained in a current report on Form 8-K to be filed by Stratus with the U.S. Securities and Exchange Commission.

Jones Walker LLP and Sidley Austin LLP are acting as legal counsel to Stratus.

About Stratus Properties Inc.

Stratus is a diversified real estate company engaged primarily in the acquisition, entitlement, development, management, operation and sale of commercial, multi-family and single-family

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residential real estate properties, and the operation of hotel and entertainment businesses located in the Austin, Texas area and other select, fast-growing markets in Texas.

Investor Contact

William H. Armstrong III

512-478-5788

Media Contact

Sydney Isaacs / Abernathy MacGregor

713-817-9346 / SRI@abmac.com

CAUTIONARY STATEMENT REGARDING FORWARD-LOOKING STATEMENTS. This press release contains forward-looking statements, which are all statements other than statements of historical fact. The words “anticipates,” “may,” “can,” “could,” “plans,” “believes,” “potential,” “possible,” “estimates,” “expects,” “projects,” “targets,” “intends,” “likely,” “will,” “should,” “to be” and any similar expressions are intended to identify those assertions as forward-looking statements. Forward-looking statements include Stratus’ intention to engage in an exploration of conversion to a REIT, potential benefits of conversion to a REIT, and statements related to the operation, benefits or effects of the Rights Plan, including the ability of the Rights Plan to preserve Stratus’ REIT status.

Stratus cautions readers that forward-looking statements are not guarantees of future performance, and its actual results may differ materially from those anticipated, expected, projected or assumed in the forward-looking statements. Important factors that could cause Stratus’ actual results to differ materially from those anticipated in the forward-looking statements include, but are not limited to: evolving risks relative to the COVID-19 pandemic and its effects; implementation, operational, financing and tax complexities to be addressed before Stratus decides whether to pursue a REIT conversion; the ability of Stratus to qualify as a REIT, which involves the application of highly technical and complex provisions of the Internal Revenue Code of 1986, as amended; Stratus’ ability to complete the steps that must be taken in order to convert to a REIT and the timing thereof; the potential costs of converting to and operating as a REIT; whether Stratus’ Board will determine that conversion to a REIT is in the best interests of Stratus’ shareholders; whether shareholders will approve changes to Stratus’ organizational documents consistent with a public REIT structure; 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, 2019, and Quarterly Report on Form 10-Q for the quarter ended June 30, 2020, each filed with the U.S. Securities and Exchange Commission.

Stratus can provide no assurance as to when, if at all, it will convert to a REIT. Stratus can give no assurance that its Board will approve a conversion to a REIT, even if there are no impediments to such conversion. Stratus’ exploration of a potential REIT conversion may divert management’s attention from traditional business concerns. If Stratus determines to convert to a REIT, Stratus cannot give assurance that it will qualify or remain qualified as a REIT. If Stratus elects to convert to a REIT, Stratus can provide no assurance that its Board will declare, or that Stratus will be able to make, future distributions to shareholders.

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 more frequently than quarterly 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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