Exhibit 5.1

[LETTERHEAD OF GOODWIN PROCTER LLP]

December 20, 2019

EastGroup Properties, Inc.

400 W. Parkway Place, Suite 100

Ridgeland, Mississippi 39157

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-3 (File No. 333-235639) (as amended or supplemented, the “Registration Statement”) filed on December 20, 2019 with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), relating to the issuance and/or sale from time to time of, among other securities, common stock, par value $0.0001 per share (the “Common Stock”), of EastGroup Properties, Inc., a Maryland corporation (the “Company”). The Registration Statement became effective upon filing with the Commission on December 20, 2019. Reference is made to our opinion letter dated December 20, 2019 and included as Exhibit 5.1 to the Registration Statement. We are delivering this supplemental opinion letter in connection with the prospectus supplement (the “Prospectus Supplement”) filed on December 20, 2019 by the Company with the Commission pursuant to Rule 424 under the Securities Act. The Prospectus Supplement relates to the offering by the Company of up $750,000,000 in shares (the “Shares”) of the Company’s Common Stock covered by the Registration Statement.

The Shares may be offered and sold from time to time pursuant to the terms of seven separate sales agency financing agreements, each dated December 20, 2019 (collectively, the “Sales Agency Financing Agreements”) with each of BNY Mellon Capital Markets, LLC, BofA Securities, Inc., BTIG, LLC, Jefferies LLC, Raymond James & Associates, Inc., Regions Securities LLC and Wells Fargo Securities, LLC, as sales agents, relating to issuances, offers and sales of the Shares.

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinion set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinion set forth below, on certificates of officers of the Company.

For purposes of the opinion set forth below, we have assumed that the Shares are issued for a price per share equal to or greater than the minimum price authorized by the Company’s board of directors prior to the date hereof (the “Minimum Price”) and that no event occurs that causes the number of authorized shares of Common Stock available for issuance by the Company to be less than the number of then unissued Shares that may be issued for the Minimum Price.

EastGroup Properties, Inc.

December 20, 2019

Page 2

The opinion set forth below is limited to the Maryland General Corporation Law.

Based on the foregoing, we are of the opinion that the Shares have been duly authorized and, when issued, delivered and paid for in accordance with the Sales Agency Financing Agreements and in exchange for a price per share equal to or greater than the minimum price authorized by the Company’s board of directors, will be validly issued, fully paid and nonassessable.

This opinion is being furnished to you for submission to the Commission as an exhibit to the Company’s Current Report on Form 8-K relating to the Shares (the “Current Report”), which is incorporated by reference in the Registration Statement. We hereby consent to the filing of this opinion letter as an exhibit to the Current Report and its incorporation by reference and the reference to our firm in that report. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/s/ GOODWIN PROCTER LLP

GOODWIN PROCTER LLP