Jelavic quickly won over the Goodison Park faithful with some early goals following his arrival from Rangers in January in 2012 - scoring the winner against Tottenham on his first start - and finished that season as the club's top scorer.
However, he saw his form dip the following season, and has since seen loan signing Romelu Lukaku preferred by Roberto Martinez this term.
The Croatia international is hoping a new start - and regular appearances - for Hull will boost his chances of making the World Cup squad.
"I'd like to take this opportunity to thank the Everton fans from the bottom of my heart for their support," he said.
"They gave me their backing from day one and never stopped believing in me, which is something I will always remember.
"I believe the scoring run which I went on during those first six months (scoring 11 times in 16 appearances) is the real Nikica Jelavic and I'm pleased the Evertonians were able to see and appreciate what I'm really about.
"Everton supporters have a special way of making you feel like one of them, and even when I was not in the team in more recent times I always felt they were behind me.
"Playing for Croatia is something I also take huge pride in and with a World Cup on the horizon I was in the situation of needing to play more games to make sure I remain in Niko Kovac's thoughts.
"Unfortunately that wasn't happening at Everton, and Roberto Martinez was very honest and up front with me about his thinking.
"When I went to meet Steve Bruce I realised it was the right move to a club with the potential to become a top Premier League outfit. Steve's ambition was clear, as was his desire to see me playing and scoring goals.
"While I'm sad to wave farewell to Everton and all my friends; it is time for my next challenge.
"I'm only pleased that I was able to say goodbye with two goals in the FA Cup win against QPR, and share some special celebrations with them one last time.
"I hope to be celebrating many more goals in future, and I'm excited to get going at my new club. But you can guarantee the Toffees will remain in my heart. I hope they can go on to fulfil their ambitions this season and I will always look out for them.
"Thank you and good luck."