The deal is believed to be worth £6.5m with a further £1m due if the Tigers avoid relegation, eclipsing the club's previous biggest outlay of £5.25m for Tottenham's Tom Huddlestone last year.
Jelavic was allowed to leave Goodison Park by Roberto Martinez in order to pursue his World Cup ambitions with Croatia after falling out of the first-team picture following the summer loan signing of Romelu Lukaku.
After scoring 36 goals in 54 games for Rangers, Jelavic made a stunning start to his Everton career following a £5.5m move in January 2012, scoring the winner on his full debut against Tottenham and going on to hit 11 goals in 16 games before the end of the season.
But he has struggled to follow that up and scored just twice for Everton this season, both goals coming in the 4-0 FA Cup win over QPR earlier this month.
"As soon as the manager called me, I realised straight away that he was really interested in signing me and that it is a great opportunity for me to come here," Jelavic told the Hull City website.
"It is a good club, and we have a good squad. We talked a little bit, but it didn't take long to realise that it was right for me.
"It's a newly-promoted club, but I can see straight away that there is a lot of ambition here within the club and I hope that we can build on the great start to the season and become a really strong Premier League team over the coming years."