The couple were caught out by the rapid flooding in the town of Sant Llorenc des Cardassar as they were travelling.
Reports in the Spanish media, citing local authorities, suggest at least three others are thought to have died in the floods.
Images on social media show cars being washed away by flood water and homes in the town submerged, with residents taking to rooftops to escape the torrents.
An emergency services spokesperson, quoted by Mail Online, said: “Five people, including two British nationals, have died.
“The British victims were travelling in a taxi that was swept away by flash floods. Their bodies were found inside the vehicle.”
It is understood the taxi driver is still missing.
Rosario Sanchez, central government representative to the Balearics, wrote on Twitter: “My condolences and solidarity for all those affected, especially the families and friends of those who have died. Thank you and my support to those who continue working.”
A Foreign Office spokesperson said: “We are in contact with the Spanish authorities responding to flooding in Majorca, and urgently seeking updates from them.”
The Foreign Office later updated its official travel advice for Spain in light of the floods.
"There have been flash floods in the island of Mallorca overnight on October 9-10 causing significant disruption and some road closures," said the FCO.
"You should follow the advice of local authorities. The emergency services number is 112."
