The National Mall features monuments to presidents and several museums that are part of the Smithsonian.
The black history museum "is in the mainstream of American history, and this site is in the mainstream of the other museums," Walter E. Massey, a Smithsonian board member, said Monday.
Chief Justice John Roberts, who serves as chancellor of the Smithsonian Board of Regents, presided over the voice vote choosing the site.
Smithsonian officials said the five-acre site would likely include a 350,000 square-foot building. That would be comparable in size to the institution's National Museum of the American Indian, also located on the mall.
"It will tell the stories of African-American culture from slavery through civil rights," said Lonnie G. Bunch, the museum's director.
Officials hope to select a design firm and complete construction in less than a decade. The federal government is expected to cover half the cost, which could top $400 million, with the balance provided through private sources and public donations.
Roger W. Sant, chairman of the regents' executive committee, cited the importance of the National Mall in the history of all Americans in the decision to locate the museum close to one of the nation's most recognizable symbols. He promised that the design would be sensitive to the location.
President Bush signed legislation in 2003 calling for selection of a site for the museum. An advisory council considered three other sites in the capital.