The former England boss endured a fractious relationship with the club's hierarchy in recent weeks and was fuming after a re-structure of his backroom staff.
"On behalf of the chairman, board of directors and Mr Moshiri, I'd like to thank Sam for the job he has done at Everton".
The 63-year-old said that he was "disgusted" by the behaviour of the board after they failed to inform him of the imminent changes, and suggested that his own future is likely to be decided during a meeting with club owner Farhad Moshiri today.
Everton have also been interested in Shakhtar Donetsk coach Paulo Fonseca, although he is also a contender to replace David Moyes at West Ham.
The club apologised to Allardyce in April after a survey was sent to fans asking them to rank their manager's performance on a scale of zero to 10.
Everton fire manager Sam Allardyce after six months
"The club is convinced the appointment of Silva was the right one and had it not been for the unwarranted approach by a Premier League rival for his services we would have continued to prosper under his leadership".
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.
A statement was released on Everton's website this morning to announce the decision with chief executive Denis Barrett-Baxendale stating the decision was taken "as part of our longer-term plan".
Allardyce, who passed 1,000 games in charge of an English club in January, said he was "disgusted" by the club's decision to make the changes public without his knowledge, according to the Liverpool Echo.