The Croatian has rarely featured for Everton since Roberto Martinez took the reins in the summer, prompting the Tigers to attempt to boost their goalscoring options.
The Croatia international has struggled for minutes under Roberto Martinez this season, appearing just 10 times for the Toffees and scoring just twice.
Both of those goals came in the club's FA Cup third round tie with QPR last Saturday while the four appearances prior to that have come from the substitute's bench.
A statement on the Everton official Twitter account read: "Everton agree a fee with Hull for permanent transfer of Nikica Jelavic and give permission for him to speak to the Tigers."
Steve Bruce's side is 11th in the Premier League goalscoring charts, a position which was boosted by the club's 6-0 win over Fulham recently, and Hull has been linked with West Brom's Shane Long in recent days.
Robbie Brady is the Tigers' top league goalscorer with just three in his 13 appearances, while frontman Danny Graham has struggled to find the back of the net with just a solitary strike to his name, forcing Bruce to seek out reinforcements.
Jelavic has been allowed to leave Goodison Park by Martinez after slipping behind Chelsea loanee Romelu Lukaku in the battle for first-team selection.
The former Rangers man made a stunning start to life in the Premier League, scoring nine goals in his first 13 top-flight outings.
But the goals have since dried up, and he will be hoping a change in scenery boosts a return of just seven from the following 46.