The British victims have been named locally as Anthony and Delia Green, a couple in their 70s.
They reportedly died along with a taxi driver when the car they were in was swept away by a torrent near the coastal resort of S’Illot.
A Dutch woman was also among the victims who were found on Wednesday.
Emergency services, assisted by the military, were said to be searching for a five-year-old boy who has been missing since the disaster.
Torrents of brown water swept cars along narrow streets in the eastern town of Sant Llorenc late on Tuesday, as rivers burst their banks and swamped homes.
Some parts of the island were hit by up to 9in (23cm) of rainfall in a matter of hours.
Mr Green, 77, and his wife, 75, were being driven to a hotel in Cala Bona when the taxi was caught by the floodwaters, Diario de Mallorca reported.
Rescue workers reportedly found the car submerged and on its side at the mouth of the torrent in S’Illot at 2am (1am BST) on Wednesday.
Military divers found the couple’s bodies still inside, while their driver, Juan Sillero, was later found lifeless nearby, the paper said.
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.”
On Wednesday, residents swept water and mud out of their houses as the floods subsided, leaving roadsides strewn with wrecked cars and trucks.
“It’s been a huge storm ... we realised that we could not control the water,” a senior official from the San Llorenc mayor’s office, Antonia Bauza, told radio station Cadena Ser.
“The situation is a disaster and we’re trying to locate survivors and help people but everything is flooded and people cannot leave their homes.”
Spain’s prime minister, Pedro Sanchez, visited the rescue coordination centre, spoke to emergency workers, and offered condolences to the victims.
“The most important thing right now is to find the missing people and respond to the concerns of their families and to everyone who lives near the affected areas,” he said. “We will be there to support them at this difficult time.”
Authorities said 80 soldiers and seven vehicles from the military’s emergency unit had joined more than 100 rescuers in the area on Wednesday.
Tennis great Rafael Nadal, who is from the island, was seen joining in with the clean-up effort. He invited locals to take shelter at his tennis academy in nearby Manacor and then joined other volunteers.
Additional reporting by agencies
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