Conservative British lawmaker Tom Tugendhat, who heads Parliament's Foreign Affairs Committee, said the loan was a "fantastic gesture of goodwill" by France.
Levi Roach, a medieval historian at the University of Exeter, said the tapestry was a symbol of the "close yet fraught" relationship between Britain in France. Its loan is especially resonant as Britain prepares to leave the European Union and strike up new relationships with its European neighbours.
"It is very significant that the Bayeux Tapestry is going to be coming to the United Kingdom and that people are going to be able to see this," May told lawmakers in the House of Commons.
May's spokesman would not comment on whether Britain planned to loan France anything in return.
The venue where the tapestry will be displayed in Britain hasn't been announced. But the Daily Telegraph understands the tapestry is destined to go on show at the British Museum in 2022, after curators have been in discussion with their French colleagues for some time.
"This would be a major loan, probably the most significant ever from France to the UK," museum director Hartwig Fischer said.
The tapestry depicts the invasion from the victorious French standpoint, but many historians believe it was stitched in England. The artefact, dating from 196BC, carries inscriptions in Greek and Egyptian that first enabled hieroglyphics to be deciphered.
- AP