Exhibit 24 POWER OF ATTORNEY Know all by these presents, that the undersigned hereby constitutes and appoints each of Staci Tyler, Michelle Rayner, Ceejaye Peters and Whitney Denham, signing singly, as the undersigned’s true and lawful attorney-in-fact to: 1. Prepare, execute in the undersigned’s name and on the undersigned’s behalf, and submit to the U.S. Securities and Exchange Commission (the “SEC”) a Form ID, including amendments thereto, and any other documents necessary or appropriate to obtain codes and passwords enabling the undersigned to make electronic filings with the SEC of reports required by Section 16(a) of the Securities Exchange Act of 1934 (the “Exchange Act”) or any rule or regulation of the SEC; 2. Execute for and on behalf of the undersigned, in the undersigned’s capacity as an officer, director and/or stockholder of EastGroup Properties, Inc., a Maryland corporation (the “Company”), Forms 3, 4, and 5 in accordance with Section 16(a) of the Exchange Act and the rules thereunder; 3. Do and perform any and all acts for and on behalf of the undersigned which may be necessary or desirable to complete and execute any such Form 3, 4, or 5, complete and execute any amendment or amendments thereto, and timely file such form with the SEC and any stock exchange or similar authority; and 4. Take any other action of any type whatsoever in connection with the foregoing which, in the opinion of such attorney-in-fact, may be of benefit to, in the best interest of, or legally required by, the undersigned, it being understood that the documents executed by such attorney-in-fact on behalf of the undersigned pursuant to this Power of Attorney shall be in such form and shall contain such terms and conditions as such attorney-in-fact may approve in such attorney-in-fact’s discretion. The undersigned hereby grants to each such attorney-in-fact full power and authority to do and perform any and every act and thing whatsoever requisite, necessary, or proper to be done in the exercise of any of the rights and powers herein granted, as fully to all intents and purposes as the undersigned might or could do if personally present, with full power of substitution or revocation, hereby ratifying and confirming all that such attorney-in-fact or such attorney-in-fact’s substitute or substitutes, shall lawfully do or cause to be done by virtue of this power of attorney and the rights and powers herein granted. The undersigned acknowledges that the foregoing attorneys-in-fact, in serving in such capacity at the request of the undersigned, are not assuming, nor is the Company assuming, any of the undersigned’s responsibilities to comply with Section 16 of the Exchange Act. This Power of Attorney shall be automatically revoked with respect to any and all of the foregoing attorneys-in-fact, with no further action required by the undersigned or the Company, in the event that such attorney-in-fact ceases to be an officer of the Company, but shall otherwise remain in full force and effect until the undersigned is no longer required to file Forms 3, 4, and 5 with respect to the undersigned’s holdings of and transactions in securities issued by the Company, unless earlier revoked by the undersigned in a signed writing delivered to the foregoing attorneys-in-fact. IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be executed as of this 25th day of May, 2023. Signature: /s/ Brent Wood Print Name: Brent Wood