Media reports estimated the transfer fee to be around eight million pounds.
Jelavic, 26, started his first-team career at Hajduk Split before having spells at Zulte Waregem in Belgium and Rapid Vienna before joining Rangers in 2010.
He scored 36 goals in 55 matches for the Ibrox side.
Jelavic becomes Everton's third signing in the January transfer window after the arrivals of Ireland midfielder Darron Gibson from Manchester United and American midfielder Landon Donovan on loan from LA Galaxy.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.