It says the British Embassy on Sunday turned over the collection including a 3,000-year-old axe, a rare first-century carved ivory elephant and an early stone Buddha statue.
Afghanistan's Foreign Ministry says the 843 pieces date from the Bronze Age to the Islamic period. Some were confiscated from smugglers, others found in private collections. The British Museum gathered the items for return.
Afghanistan National Museum director Omara Khan Massoudi says some of the artifacts will soon be on display to the public.
It is the second huge handover of Afghan historical pieces by the British Museum. In 2009, about 1,500 historical pieces were returned.