A Miami investment fund is about to close on its purchase of the Trump family’s rights to an opulent Washington, D.C., hotel, paying $375 million and beginning the process of rebranding the property as a Waldorf Astoria.

CGI Merchant Group agreed to buy the lease to the property in November. The hotel is owned by the federal government, but with extensions the lease runs close to 100 years. It is housed in the former Old Post Office, which is located a short walk down Pennsylvania Avenue from the White House.

The sale could close as early as next week, according to people familiar with the matter. The new owner plans to temporarily shut down the hotel, remove the Trump name, and reopen it in June as a Waldorf Astoria hotel, these people said.

The property will be managed by Hilton Worldwide Holdings Inc., which owns the Waldorf brand. During the weeks the hotel is closed, Hilton will install its own property-management systems and train staff, who are expected to stay on under the new management team, these people said.

Donald Trump, breaking with recent precedent, didn’t sell his businesses after being elected president. Instead, he placed his holdings in a trust run by his sons. That sparked criticism from Democrats and watchdog groups, which said that owning properties where foreign, federal, state and local governments spend money could violate constitutional bans on the president’s receiving “emoluments”—things of value—beyond his fixed salary.

The Trump Organization has said it didn’t market the hotel to foreign dignitaries and that it wrote a check to the U.S. Treasury Department for money made from foreign-government guests.

Eric Trump, the former president’s son and an executive vice president of the family company, told The Wall Street Journal in 2019 that scrutiny of the hotel’s profits was one of the reasons the family decided to market the hotel that year.

The Washington hotel has been a jewel in the Trump family portfolio. In 2012, the Trumps beat out some of the most-experienced and deepest-pocketed names in the lodging business, including Marriott International Inc. and Hilton, for the rights to the lease with the highest offer.

The hotel became a popular meeting spot for Republican lobbyists, lawmakers and staff. How much money it made has been in dispute. A report last year from the House Committee on Oversight and Reform, which had been examining the lease terms between the Trump Organization and the federal government’s General Services Administration, said the hotel lost more than $70 million between its opening in 2016 and 2020. The Trumps have disputed those findings.

The sale represents a second chance for Waldorf Astoria at that location. The hotel boasts some of the largest hotel rooms in the capital and suites with 18-foot ceilings.

“We continue to recognize the opportunity for growth in the nation’s capital and hope to have more to share soon,” a Hilton spokeswoman said.

Hotels that cater to business travelers have struggled during the Covid-19 pandemic, and Washington has been hit harder than most cities. Its revenue per available room, a primary industry metric, was down 49% last year, compared with 2019, according to hotel data tracker STR. For the top 25 markets in the U.S. excluding Washington, revpar was down about 32% last year, compared with 2019.

CGI, which has joined with former baseball superstar Alex Rodriguez on its hotel investments, emphasizes more socially conscious investing. The firm has pledged that properties in its Conscious Certified Hotels collection, which includes the Gabriel in Miami Beach, will donate 1% of all room revenue to local nonprofit organizations, according to the company’s website.

Write to Craig Karmin at craig.karmin@wsj.com