The two clubs agreed a fee for the Croatia international and former Rangers player on Friday and all that remains is for personal terms to be finalised.
Everton boss Roberto Martinez has allowed Jelavic to leave to help his World Cup fortunes as the striker has been reduced to a bit-part player at Goodison Park after the loan signing of Romelu Lukaku.
"Steve Bruce called me and told me that he wants me in his team as a leading attacker," Jelavic told Croatian newspaper Jutarnji list.
"He asked me if I'm ready to move, then talked briefly about the club, his coaching philosophy and about the club's goals.
"He was very confident during that conversation and after that I agreed to move to Hull City.
"The club suits me and I'm happy that the clubs have found an agreement for my transfer."