The 28-year-old will head to Yorkshire for a medical and to agree personal terms over the weekend, representing Hull boss Steve Bruce's first foray into the transfer market this month.
Hull have impressed on their return to the Premier League and sit 10th after 20 games, although they have been far from prolific.
With a total of 22 goals - including six put past Fulham in one game - Hull's top scorer in the league is Robbie Brady with three to his name, all of which came within the first six games of the campaign.
A striker has been high on Bruce's list of priorities, with a long-term pursuit of Shane Long being routinely rebuffed by West Brom.
Jelavic has been allowed to leave Goodison Park by Roberto 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.
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