The 25-year-old was offered a contract extension by Frank Lampard's side, but has opted to leave Merseyside in search of regular first-team football elsewhere.
However, backup goalkeeper Asmir Begovic has seen a one-year option triggered in his contract to keep him at Goodison Park for the time being, whilst fellow shot stopper Andy Lonergan has been offered a new deal to extend his stay as well.
A statement on the official club website on Saturday said: "Ahead of the release of the Premier League retained lists, Everton have taken up the option to extend Asmir Begovic's deal for a further year - and offered a new contract to fellow goalkeeper Andy Lonergan.
"Jonjoe Kenny was also offered fresh terms but has decided to move on in pursuit of a new opportunity elsewhere."
After joining the Everton academy at the age of nine, Kenny spent 16 years with the club, making 50 Premier League appearances during that time following loan spells with the likes of Celtic and Schalke in recent years.
Begovic made seven appearances for the club across all competitions during the 2021-22 campaign, following his free transfer move from Bournemouth last summer, with the Bosnian playing backup to England goalkeeper Jordan Pickford at Goodison Park.
Meanwhile, Everton also announced that 10 youth players have been offered new deals this summer, including Lewis Gibson.