Everton have given the Tigers permission to open talks with the Croatia international over a possible move to the KC Stadium.
The 28-year-old, who moved to Goodison Park from Rangers in a £5.5m deal two years ago, has struggled to earn a regular place in the first-team under Roberto Martinez this season.
Jelavic has made only 10 Premier League appearances, and he scored his first goals of the season in the 4-0 FA Cup win over QPR at the weekend.
Hull boss Steve Bruce has put Jelavic top of his January hit-list in a bid to solve his shortage of strikers, and the Tigers will now attempt to agree personal terms with the forward over the next few days.
A statement on the Hull website read: "Hull City have reached an agreement with Everton over the transfer of striker Nikica Jelavic and will now enter talks with the player.
"The 28-year-old Croatian international has scored 21 goals in 69 appearances for Everton since joining them from Rangers in January 2012."
Jelavic has been linked with a number of clubs since the transfer window opened, with Premier League strugglers West Ham and Crystal Palace both rumoured to be interested.
Bruce has been seeking to add firepower to his team, but on Thursday he apologised to both West Brom and Sunderland for reports linking the Tigers with moves for Shane Long and Steven Fletcher respectively.
He insisted in that press conference that the club had not made bids for any players, but a little over 24 hours later Everton have given them permission to open talks with Jelavic.