Tosun scored 20 goals in 33 league appearances last term to steer Besiktas to the title and has netted another eight in 16 appearances this term.
His arrival brings an end to the club's long hunt for a replacement for Romelu Lukaku, who left to join Manchester United in a £100m deal last summer.
I know the guys as I've always watched Everton's games from Turkey, so I know a bit about the team already.
Tosun will know how his quickness, instincts and versatility will set him apart in an Everton squad lacking match-winners up top.
"I bring my skills here and everybody is going to see what kind of player I am", he said.
The Turkish worldwide has signed a four-and-a-half year deal at Goodison Park in a move understood to have cost in the region of £27 million. "He is Turkey's No. 1 striker and has scored goals in the Champions League and the Turkish League but he is desperate to play here in the Premier League".
"They are professional enough today to know what the size of the game is and make sure they try to deliver the best on Friday night".
Davy Klaassen was considered a high profile signing when he arrived from Europa League finalists Ajax back in June, but having not featured in a single Premier League game under Sam Allardyce the impression is that already his days on Merseyside are numbered.
For his part, Allardyce does not feel he could have done a better deal.
He said he really wanted me here and to feel that, of course, is another big reason to come to Everton. He has got some good movement, he's two-footed, he's not the biggest but he's efficient in the air in the box. But we can't have researched any more and can't have looked at the qualities of the player more, not just from a talent and goalscoring point of view but from the mentality side too. "I do not think you can look any more than we have done".