The 24-year-old attacking midfielder has returned to the club where he spent a year on loan before joining Spurs in 2012.
Sigurdsson has moved to the Liberty Stadium on a four-year contract, part of a deal which has seen Swansea duo Ben Davies and Michel Vorm move to White Hart Lane.
And he said: “It’s great. I really enjoyed my time here last time. As soon as there was interest I was very happy, and it was an easy decision to come.
“I know the club, the manager, the players, the fans and the city. But the way they play football was a big factor too.
“They have got some great players here and the manager has told me the squad is getting stronger. Hopefully we will be better than last year and can get back to the top half of the table, where Swansea belong.”
Sigurdsson signed for Tottenham under previous manager Andre Villas-Boas and he scored 13 goals in 83 appearances in his two seasons at the club.
But after seemingly being surplus to requirements under new boss Mauricio Pochettino, the former Reading man joins Swansea with former team-mate Garry Monk now in charge.
And he said: “I think the main aim for the club is obviously to stay in the Premier League.
“We want to push on even further and get the club back into the Europa League, where it was last season. Hopefully, we can finish in the top half of the table.“I enjoyed my two seasons at Tottenham, so it’s difficult to leave, but as soon as I heard Swansea were interested – that was the club I wanted to play for.”