The cost of the deal was undisclosed, however, the Spurs have offered a five-year contract for Davies while Vorm got a four-year one.
The London club updated on their latest signing on the social-networking site twitter, tweeting: “We are delighted to announce that we have reached agreement with Swansea City for the transfers of Ben Davies and Michel Vorm.”
The duo had been among Tottenham Hotspurs’ top transfer targets this season with the defender Ben Davies having impressed with his performances since his arrival at Swansea.
Davies said after the signing: "I had never thought or wanted to leave Swansea, but an opportunity like this doesn’t come up often in your career.
“I will always be grateful for what Swansea City has done for me and it will always be the club in my heart.
“Having been at the club since the age of eight, I had to think long and hard about leaving because I owe everything to the staff and the club in general”, concluded the Welshman.