Anthony and Delia Green, both in their 70s, died on Wednesday when their taxi was swept away by a torrent of water near the coastal resort of S’Illot.
So far authorities on the popular tourist island say 10 people have died after torrential rain deluged the region around the town of Sant Llorenc, about 40 miles east of the capital, Palma.
A Foreign Office spokesman said: “We are supporting the family of two British people following their deaths in Spain, and will do all we can to assist them at this deeply difficult time.
“Our staff remain in contact with the Spanish authorities who are responsible for responding to the floods, and are ready to assist any other British people who require our help.”