The Croatian striker signed a three-and-a-half-year deal with Hull on Wednesday in a bid to gain more match time ahead of the 2014 FIFA World Cup.
And, while believing the opportunity to move to the KC Stadium was too good to turn down, Jelavic - who joined Everton from Rangers in January 2012 - admitted he would leave Goodison Park with a heavy heart.
"I’d like to take this opportunity to thank the Everton fans from the bottom of my heart for their support," read the letter, published in the Liverpool Echo on Thursday.
"They gave me their backing from day one and never stopped believing in me, which is something I will always remember.
"To score on my full debut in that memorable game against Tottenham was very special, and the feeling of Goodison that night will remain with me.
"I believe the scoring run which I went on during those first six months 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."
Jelavic went on to stress that his place in Croatia's World Cup squad was at the forefront of his thoughts as he made the decision to join Steve Bruce's side.
"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 ahead of the tournament in Brazil,” he continued.
"Unfortunately that wasn't happening at Everton, and Roberto Martinez was very honest and upfront 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.
"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.
"Hvala vam i sretno (Thank you and good luck)."
