The record-setting SpaceShipOne is due to arrive in its final resting place, the Smithsonian's National Air and Space Museum (NASM) in Washington DC.
SpaceShipOne will go on public display some time this year
The suborbital rocket plane, designed by Burt Rutan and his Scaled Composites team, made two piloted trips into space to claim the $10m Ansari X-Prize.
SpaceShipOne is to be displayed in the museum's Milestones of Flight Gallery, according to a NASM spokesman.
The gallery exhibits some of the major firsts in aviation and space history.
Among other aviation "stars", SpaceShipOne will keep company with the Wright Brothers' 1903 Flyer and the Apollo 11 command module "Columbia", which carried the first man to the Moon.
Voyager, another Burt Rutan design, which completed the first non-stop non-refuelled flight around the world, hangs in the south lobby of NASM.
SpaceShipOne rocketed into history on 4 October, 2004, becoming the first privately owned spacecraft to exceed an altitude of 100km (328,000ft) twice within the space of a 14-day period, thus claiming the much coveted Ansari X-Prize.
It had previously become the first private manned spacecraft to fly to the edge of space and back in a test mission in June.
No specific date has been set for the craft to go on public display at the museum, but it will be some time this year, the NASM has said.