The 27-year-old joins from fellow Premier League side Swansea City for a fee that could rise to £45-million (R765-million).
Sigurdsson has spent the past three seasons with Swansea and was directly involved in 21 Premier League goals last term. He also covered the greatest distance of any top-flight player during the season – 433 kilometres – and has been directly involved in 53 league goals since the start of 2014/15 – second only as a midfielder to Tottenham’s Christian Eriksen.
“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 teammates 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.”
Everton manager Ronald Koeman was delighted to land a player he revealed had been in his sights for some time.
“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.”