The Iceland international, 27, has inked a five-year deal at the Toffees, putting to bed a drawn-out process between the two clubs.
Sigurdsson had been on Everton's radar for over a year and the Merseysiders reportedly had two bids previously knocked back by Swansea.
However, Everton have now finally secured their man — increasing their summer spending to well over £100m after also signing the likes of Jordan Pickford, Michael Keane and Wayne Rooney this summer.
Sigurdsson — who scored nine goals and registered 13 assists in the Premier League last season — missed a large chunk of Swansea's pre-season due to the ongoing speculation surrounding him.
Leicester City were also keen on landing Sigurdsson, with the Foxes having reportedly had an offer rejected by Swansea in July.
"Hopefully I will continue to create goals and score goals for the team and contribute to the kind of success we’re seeking at the club," Sigurdsson told EvertonTV.
"This is an ambitious club and it is clear we are moving in a really good direction. The most important thing is that this team keeps winning games and climbing the table — and does that throughout the season.
"For myself, I would like to score as many goals as possible and create as many goals for my team-mates as I can. These are my targets.
"But it is always the same thing: as long as the team is winning I will be more than happy."
Look who's here... pic.twitter.com/iAcnN5SSn4— Everton (@Everton) August 16, 2017
And manager Ronald Koeman was thrilled to land his man.
"I'm really happy because the board and especially our chairman, Bill Kenwright, did everything to get him. It took some time but finally we have signed the player," Koeman said.
"In my opinion, in his position he is one of the best in the Premier League. We have the player here and that's really good for the team."