The Iceland international has signed a five-year deal at Goodison Park, keeping him there until June 2022, and his new head coach believes that he will add "productivity" to the team.
"I'm really happy because the board and especially our chairman, Bill Kenwright, did everything to get him," Koeman told Everton TV.
"It took some time but finally we have signed the player. Of course, from the beginning, he was one of the key players we wanted to bring to Everton. That's because of his quality first and foremost and his experience in the Premier League.
"We need more productivity. We don't sign one player who will score 25 goals but we need several players around our striker to get that number. He is one of those productive players - he's shown that at Swansea and also in the past. In my opinion, in his position, he is one of the best in the Premier League."
Sigurdsson, who is believed to have cost Everton £45m, has become the club's eighth summer signing.