Vorm, 30, joins first choice France goalkeeper Hugo Lloris, who signed a new five-year deal with Spurs after the World Cup, and U.S. veteran Brad Friedel, 43, at the club. No fees were disclosed.
Friedel is staying with Spurs in a coaching and part-time playing capacity.
"Every club has two top goalkeepers in their squad," Dutchman Vorm told De Telegraaf newspaper on Wednesday.
"It suits the club's philosophy that there are two of us with Hugo and me. Especially when we see that Tottenham is active in a lot of competitions."
Vorm has played 15 times for his country and made one appearance for the Netherlands at the World Cup, coming on for the last two minutes of their 3-0 third place playoff win over Brazil.
Vorm and full back Davies are new manager Mauricio Pochettino's first signings since the Argentine joined the club last month from fellow Premier League club Southampton.
Davies has been training with his new team mates in Toronto while the paperwork on his deal was completed.
Sigurdsson, 24, returns to Swansea having scored seven goals in 18 games during a successful loan spell from German club Hoffenheim in the club's debut Premier League campaign in 2011-12.
(Reporting by Mike Collett; editing by Tony Goodson)
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