Spurs have beaten Liverpool to the Welshman's signature, while adding the goalkeeper in a double swoop, as Mauricio Pochettino makes his first foray into the transfer market
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 preseason 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.