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The forward, who has scored 41 goals in 96 Turkish Super Lig games since the start of the 2014-15 season, said boss Sam Allardyce was a key factor in his decision to move to the Premier League.
"It feels great to be an Everton player," Tosun told evertontv.
"I'm really happy to be here and happy that everything is done. I'm really excited to play for Everton as soon as possible. Everton is a great club with a big history and a big culture and I'm looking forward to showing the fans the kind of player I am."
"Sam Allardyce was a big part of my decision," he added. "He said he really wanted me here and to feel that, of course, is another big reason to come to Everton."
Allardyce is excited to have landed the Besiktas player, who will boost his options up front, where they have been short since Romelu Lukaku left the club in the summer to join Manchester Untied.
"He is Turkey's number one striker and has scored goals in the Champions League and the Turkish League but he is desperate to play here in the Premier League," said the Everton boss.
Tosun, 26, has scored eight goals for Turkey in 25 appearances.
