The Croatian declared his intention to join the KC Stadium outfit last week after struggling for first-team opportunities under Roberto Martinez this season - with just 10 appearances and two goals in all competitions.
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"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.
"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."
Hull owner Assem Allam confirmed the imminent nature of the move on Tuesday, describing Jelavic as the club's "biggest ever signing."
"The club is moving forward. We are paying a lot of money for first-class players," he told Sky Sports News.
Allam also confirmed that a move for West Brom striker Shane Long is nearing completion following a failed attempt during the summer.
He added: "We have agreed terms. It is a matter of getting the club to release and the player to agree."