In an exclusive article in tonight's Yorkshire Evening Post, the 37-year-old former Bristol Rovers, Crystal Palace, England and now Leeds keeper said: "The Leeds supporters have always been brilliant with me and I want to thank them.
"It's a bit sad that I haven't had a proper chance to say goodbye.
"I got a call after Saturday's match telling me about Everton so I haven't been able to thank the fans at a game.
"Hopefully I'll see the away supporters at Goodison in a few weeks time, but I'm already looking forward to coming back to Elland Road because I'll get a real chance to say thank you properly."
Despite losing his place in the first team over the past 12 months he has remained a popular figure with the Elland Road fans and he says he won't forget the way they took him to their hearts.
"I always remember us losing 4-0 to Manchester United in one of my first games," he recalled.
"The players who were at the club had made it clear to the new lads how important that game was, but we got trounced.
"But the fans were brilliant with me that day.
"I like to think I struck up a good rapport with them and I totally respected them because they were so good to me."
Martyn admits he is looking forward to his move to Merseyside although he and his family will still live in the Leeds area.
"This is a fresh challenge," declared Martyn. "It's been a bit frustrating and this is probably what I needed.
"I didn't want to finish my career on the bench and at Everton, hopefully, I'll have the chance to play in the Premiership again.
"It won't be guaranteed, though, and I'll have to knuckle down, work hard and, all being well, push for that number one spot."