The Iceland international has returned to the Liberty Stadium, where he scored seven goals in a loan spell from Hoffenheim in 2012, and becomes the club's fifth summer signing
The 24-year-old attacking midfielder completed a medical on Wednesday, having left Spurs' tour of the United States, before penning a four-year deal.
The Icelander struggled to hold down a starting berth at White Hart Lane, making just 26 Premier League starts in his two seasons at the club, but returns to the Liberty Stadium where he enjoyed a productive loan spell in 2012.
"I really enjoyed my time last time I was here, so it's really good to be back," he told the club's official website. "I was here for five or six months and still have a lot of memories. Hopefully this time it will be even better.
"The squad has changed a little bit, quite a lot of new players have come into the squad, but the core is still there."
Sigurdsson, then on loan from Hoffenheim, made 18 appearances under Brendan Rodgers, scoring seven goals and assisting a further three to endear himself to the Swansea faithful.
Crystal Palace were also intersted in the former Reading man, but he elected to return to south Wales and becomes the club's fifth signing of the summer after Lukasz Fabianski, Bafetimbi Gomis, Stephen Kingsley and Marvin Emnes.
The deal paved the way for left-back Ben Davies and goalkeeper Michel Vorm to join Spurs.