The Corcoran Gallery of Art’s board of trustees will announce Monday that it will distribute almost 11,000 works remaining in its renowned collection, a historic giveaway that includes paintings by Washington Color School artist Sam Gilliam, photographs by Ansel Adams and Dorothea Lange, and prints by 19th-century French master Honoré Daumier.

Almost 9,000 pieces will go to the American University Museum at the Katzen Arts Center, with others headed to 10 Smithsonian Institution museums, several universities and the U.S. Supreme Court.

The distribution marks the final stage of the dismantling of the famed Washington institution. Under a controversial 2014 deal, the National Gallery of Art had first dibs on the entire collection and ended up acquiring about 40 percent of the 19,493 works. George Washington University gained control of the museum’s independent school and its two historic buildings, including the Flagg Building on 17th Street NW.

“Having three anchors, where the bulk of the collection legacy of the Corcoran could be accessed, seemed like a great balance,” said Corcoran board chairman Harry F. Hopper III.

The artwork given to American University represents the largest piece of the Corcoran holdings and is a “once-in-a-lifetime opportunity,” said Jack Rasmussen, director and curator of the American University Museum at the Katzen. American is in the process of finalizing the acquisition.

The Corcoran works, Rasmussen said, complement the university’s focus on contemporary art and Washington artists. The major gift raises the national profile of the largest university-affiliated museum in the region.

“The Corcoran was the center of the art world in Washington, and the center of gravity has come over here a bit,” he said. “We have the facility and the interest in Washington. The Corcoran legacy is our legacy, too. It’s Washington’s ­legacy.”

The National Gallery acquired more than 8,000 pieces in 2015, including significant works by ­Albert Bierstadt, Frederic Edwin Church, Cy Twombly and Jenny Holzer, transforming its holdings of contemporary art, photography and American paintings.

In 2016, the Corcoran released a list of the remaining work to Washington institutions and encouraged them to make selections. Three independent curators reviewed the requests and offered recommendations, and the ­Corcoran board made the final decisions.

Hopper said the board was painstaking in its effort to match the works with the institutions and is donating pieces to all the organizations that asked. It is sending works to every corner of the city — from the Anacostia Community Museum in Southeast to the Kreeger Museum in Northwest — and to Georgetown and Howard universities and the University of the District of Columbia.

“The institutions had to have the capability of receiving them and being good custodians, and to not only exhibit them, but to make the works accessible,” Hopper said.

George Washington University was offered about 800 works, second behind American University. Included are works of historical interest, including a portrait of founder William Wilson Corcoran and a trowel that was used to set the cornerstone of the Flagg Building, said Kym Rice, assistant director for academic affairs at the Corcoran School of the Arts and ­Design.

“It’s a very generous and important gift to us,” she said. “It matches a lot of the strengths of GW.”

The Smithsonian American Art Museum has been offered about 320 works, including prints and graphic works by Puerto Rican artists and social documentary photography, which is a focus of its collection.

“It’s exciting for the city,” said SAAM curator Virginia Mecklenburg. “Anyone who does art historical research knows how important the Corcoran was. It’s bittersweet.”

Only 109 items, less than 1 percent of the total, are going to institutions outside Washington, ­including 92 pieces of lace to the Smithsonian’s Cooper Hewitt ­Design museum in New York.

GWU is renovating the Flagg Building, which includes galleries that will be curated by the National Gallery of Art, according to spokeswoman Anabeth Guthrie. Museum staff will spend a year monitoring the environmental conditions of the galleries before installing exhibitions sometime in 2019.