The archaeopteryx was discovered in Germany encased in limestone in 1861. It shows characteristics of both early birds and dinosaurs, with feathers, claws and teeth.
The museum is sending it to Japan as part of its biggest-ever global exhibition. Known as the "London specimen," it will go on show with 300 other exhibits at Tokyo's Museum of Nature and Science for three months from March 18.
The British museum's Prof. Paul Barrett says the fossil's "lasting historical legacy" is that it establishes birds as dinosaurs.