The Croatian striker had been linked with several English clubs in recent weeks, including the Toffees’ city rivals Liverpool and West Ham, but the former Rapid Vienna man has signed a four-and-a-half year deal at Goodison Park.
Jelavic is set to more than double his salary to £45,000-a-week, having earned £20,000-a-week at Rangers, where he scored 36 times in 55 matches.
Speaking about his move, Jelavic told Sky Sports: "My dream was to play in the Premier League so this is a dream come true. Everton is a big club, I'm just excited at the moment.
"This is the best league in the world and I want to try myself here. Of couse it will be harder to score here than in Scotland but I'm ready for the challenge.
"I'm enjoying watching the game but I'd love to be playing."
The striker was presented to fans at half-time in Everton’s home match against Manchester City on Tuesday night, and should be available for David Moyes’ side’s next match away to Wigan.
Jelavic becomes Everton’s third signing of the January transfer window following the capture of Darron Gibson from Manchester United, and the loan acquisition of Landon Donovan from MLS side LA Galaxy.