The retired orbiter, which completed 39 missions and spent more than 365 days in space, is being moved into the national aerospace collection at the museum's Steven F. Udvar-Hazy Center in Virginia, the agency reported.
"NASA and the Smithsonian signed an agreement in 1967 that has enabled the National Air and Space Museum to preserve and display the greatest icons of our nation's space history," Gen. J.R. "Jack" Dailey, director of the museum, said in a statement.
"At the Udvar-Hazy Center, Discovery will be seen by millions of people in the coming years, especially children, who will become the next generation of scientists, engineers, researchers and explorers."
Discovery was flown atop a modified Boeing 747 from the Kennedy Space Center in Florida to Washington Dulles International Airport Monday.
Before landing, the air-and-spacecraft combination took part in a historic flyover of Washington.
"As part of the Smithsonian collection, Discovery will bring a richer perspective to the historical and scientific significance of the space shuttle program, one of our country's greatest achievements," Wayne Clough, secretary of the Smithsonian, said in a statement.