But Alan Shearer said on Match Of The Day "look at the three clubs that sacked Big Sam ... Bolton, Blackburn and Newcastle ... they were all relegated! So West Ham be warned."
The 60-year-old's future in east London has been the subject of speculation for much of the season, but the club finally confirmed his exit within minutes of their final Barclays Premier League match of the season at Newcastle ending.
A tweet from the club's official Twitter account read: "The club have begun the search for a new manager after deciding not to renew Sam Allardyce's contract."
Allardyce took over at Upton Park in 2011 and the Hammers made an excellent start to the current campaign, but tailed off dramatically to finish in 12th.
The club said that joint owners David Gold and David Sullivan would now lead the process to recruit Allardyce's successor.
"We would like to start by thanking Sam Allardyce for his valuable work since arriving at the Boleyn Ground four years ago," Gold and Sullivan said.
"He leaves the club in a considerably better state then when he arrived and, for that, the board are truly grateful.
"However, we have made the decision not to renew his contract, so we now have the chance to appoint a new manager with a new philosophy to lead us into two of the most exciting years in our great club's history.
"Our target is to recruit a manager that will build a team capable of saying a fitting farewell to the Boleyn Ground next year and do justice to the outstanding surrounds we will call home from August 2016 (when the club move to the Olympic Stadium in east London).
"We have already been impressed with the quality of candidates that have expressed an interest in the role and fully expect to appoint a manager with the credentials to take this club on to new heights."
Allardyce had said on Friday that his agent Mark Curtis would be meeting with club representatives on Monday to discuss the future, with the manager himself jetting off on holiday.
''It will be all sorted Monday, one way or the other. I'm not personally having a meeting but my agent will be available to speak to the owners,'' Allardyce had said.
''Because the season is finishing so late, the only opportunity I have to go away with my grandchildren is half-term. So I'll be shooting off to Spain to see them and whatever will be, will be.''
Former West Ham defender Slaven Bilic and ex-Manchester United manager David Moyes are among those linked with succeeding Allardyce with the Hammers.
Allardyce said the decision reached was the best step for all concerned.
"I think it's right for both the club and myself," he said.
"My time has been a fantastic time. I've really enjoyed the London scene, I've really enjoyed managing the club and I've really enjoyed the success we've gained from the period of time we've been together."
He took over a relegated side in 2011 and led West Ham to promotion back to the Premier League in his last season, which he called "one of the most difficult tasks you will face".
"To move on from there and stabilise it for the big move to the new stadium is what I've done," Allardyce said on Sky Sports News.
"I've delivered everything that's been asked of me, I've enjoyed doing it.
"We've built the team to get stronger and stronger, even though we're disappointed with the last quarter of the season.
"Overall we've had a fantastic journey together: the players, my staff, the owners, the fans and everyone concerned with West Ham.
"They should hopefully look forward to a bright future.
"For me it's time to get out, get away, think about me and only me and the family for a change."
Allardyce could be back in management next season if the right offer comes along, saying that it "depends what the challenge is".
"There's no desperate need for me to be jumping back into this game," he said.