The Britons killed were travelling in a taxi which was overcome by floodwater, The Telegraph reports.
Weather forecasters reported that eight inches of rain fell in the area - 40 miles east of the capital of Palma on the Spanish island - in just four hours.
"I took refuge on the roof of a neighbour's house where I stayed for awhile", he told AFP, adding that he watched as his auto was swept away by the current.
Bauza told Cadena SER radio that two other victims were local residents, including an elderly woman whose body was found in the basement of her house.
In an emailed statement, the British government's Foreign Office 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 hard time".
A dry creek overflowed, creating a strong current of water and mud that buried cars and tore trees along the way, witnesses told Spain's TVE.
At least 10 people died on the Spanish island of Mallorca after a torrential rainstorm caused flash flooding that left a trail of piled vehicles and damaged infrastructure from surges of water and mud.
According to Diario de Mallorca, the bodies of an 81-year-old man and 83-year-old woman were among the first to be found on Tuesday.
"It all happened in less than 10 minutes", one told Spanish TV.
One of the male victims could not yet be identified but is also believed to be a foreigner.
Meanwhile tennis star Rafael Nadal, who is from the island, was seen joining in with the clean-up effort.
Marks on the walls showed flood waters reached up to a height of at least a metre (three feet).
Authorities said 80 soldiers and seven vehicles from the military's emergency unit had joined more than 100 rescuers deployed in the area on Wednesday.
Prime Minister Pedro Sanchez visited the disaster zone and described the situation as "absolutely extraordinary".
The 17-time Grand Slam victor also provided shelter at his tennis academy in Manacor for displaced people whose homes were severely damaged by the flash flood.