The 63-year-old had more success at Sunderland.
"We have made the decision that, as part of our longer-term plan, we will be appointing a new manager this summer", said new chief executive Denise Barrett-Baxendale.
Despite lifting the club from 13th in the Premier League when he took over to eighth finish, Allardyce, a former England boss, could never win over a large section of the Everton fanbase.
He is currently the hot favourite to make his return with Everton, while Shakhtar Donetsk coach Paulo Fonseca is also in the frame, alongside Louis van Gaal, whereas a certain David Moyes is now free....
Everton's board exacted sweeping changes without Allardyce's input and the manager said he was "disgusted" at the failure to consult him.
However, he was booed by fans following his side's 2-1 defeat at Burnley in March, and was again criticised after their draw with Swansea six weeks later.
Allardyce last month dismissed a survey sent to supporters asking them to grade his performance out of 10 as a mistake on the part of the club's marketing director, who he said does not "understand" how football works.
Everton scored only 44 goals in 38 outings in the league, the second lowest tally of all teams outside the bottom six, and with the future in mind, the club have decided to make a change.
England's all-time top scorer had reportedly agreed terms on a £12.5 million move to DC United in Major League Soccer last week.
"I'm shocked, disappointed and disgusted that the football club didn't have the decency to tell me, my Director of Football and my staff about the changes".