Emergency services headed to the River Esk near the town of Glaisdale shortly before midday (1200 GMT), after reports that a vehicle had fallen into the river.
"The vehicle was recovered from the river by the fire service just after 3:00 pm. Sadly, the three men inside have died," North Yorkshire Police said.
Another man who had tried to help them was recovered unharmed, it said, adding that the weather conditions were "making driving hazardous".
Several regions of the UK, particularly Scotland and northern England, have been badly hit by Storm Gerrit since Wednesday, which has brought heavy rain and snow.
Winds of up to 136 kilometres per hour (85 miles per hour) were recorded in Aberdeenshire in Scotland.
The UK's Met Office said a supercell thunderstorm caused damage in Greater Manchester on Wednesday night, with features suggesting "a tornado at the surface was likely".
Thousands of homes remained without power in Scotland on Thursday afternoon, while rail and air transport were disrupted with trains and flights cancelled.
Ferry services between Dover and France also suffered delays on Wednesday due to strong winds in the Channel.
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