Sky Sports reported on Monday that the Netherlands international was in talks with Spurs after a fee in the region of £5million was agreed for his transfer.
And Vorm, 30, will undergo a medical on Tuesday having agreed personal terms with the north London club.
Should his medical prove successful, Vorm will join up with new manager Mauricio Pochettino and his squad at the end of his extended break following the World Cup.
Both Tottenham and Swansea are currently on pre-season tours of the USA and this has allowed them to conduct lengthy, complicated negotiations involving three players.
One of those is Spurs’ attacker Gylfi Sigurdsson, and Sky sources understand he has agreed to move to Swansea in the opposite direction for similar price to that of Vorm.
It is believed the Iceland international will also have a medical on Tuesday ahead of a return to the Liberty Stadium, where he previously spent a season on-loan.
Vorm is an experienced Dutch international and a Premier League regular with the Swans, whom he joined from Utrecht in 2011, and Spurs have targeted him to strengthen their goalkeeping department.
Vorm was believed to be uncertain as to how much playing time he would get in competition with France No 1 Hugo Lloris but Tottenham are determined to have two top-class goalkeepers in competition with each other.
Lloris, 27, recently signed a new five-year deal at White Hart Lane, while Spurs’ other established keeper is the 43-year-old veteran Brad Friedel, who also signed a one-year contract extension this summer.
However Friedel, a former USA international who played in the 3-3 pre-season friendly draw with Seattle Sounders on Saturday, is expected to take on a more senior, coaching role alongside new goalkeeping coach Tony Jimenez, as well as providing first-team back-up.
Wales left-back Ben Davies, meanwhile, has been pictured in his first training session with Tottenham in Toronto having had his transfer to Spurs all but formally announced.
The clubs are expected to publicise these transfers in the coming days.