The ex-Republic of Ireland International had been at the club since 2017, arriving from Sunderland.
He was in a different role at first, but became their goalkeeping coach in late 2019.
Director of Football Kevin Thelwell said: “We would like to place on record our sincere thanks and appreciation to Alan for his significant contribution to Everton. Alan is a much liked and trusted member of the Everton family and he departs with our very best wishes, safe in the knowledge that he will always be welcome back at the Club.”
Kelly added: “I am proud to have served Everton as a goalkeeping coach since 2017.
“I‘ve had the pleasure of working with many talented goalkeepers from the Academy to the First team and I sincerely thank them all for their attitude, hard work and trust. I loved every minute out on the training pitch with you and that bond will be there for a lifetime.
“I would like to wish the players, fans, and the Club the very best of luck for the future.”