The Wales and Netherlands internationals become new boss Mauricio Pochettino's first signings, with the defender penning a five-year deal and Vorm agreeing a four-year contract.
Davies had been expected to move to Anfield, lured by the appeal of Champions League football, but Spurs gazumped the Reds by promising the 21-year-old a regular starting berth.
The deal was hastened due to both Tottenham and Swansea being on pre-season tours in the United States, with Davies linking up with his new club in Seattle to undergo a medical.
The defender came through the academy at Swansea, displacing Neil Taylor to establish himself at the club's undisputed first-choice left-back two years ago.
Vorm has impressed since moving to the Premier League three years ago from Utrecht, helping the Swans - along with Davies - to the Capital One Cup in 2012-13.
The 30-year-old will now provide cover for first-choice goalkeeper Hugo Lloris at White Hart Lane.
The deal paved the way for Gylfi Sigurdsson to return to the Liberty Stadium, having spent time there on loan from Hoffenheim.