West Ham manager Slaven Bilic was sacked on Monday with the team in the Premier League drops to relegation zone.
Bilic's last game in charge was Saturday's 4-1 defeat by Liverpool at London Stadium.
West Ham said the club believed a change was necessary "to move forward positively and in line with their ambition".
Former Everton and Manchester United boss David Moyes has been strongly linked with succeeding Bilic, says a report on BBC.
Speaking to reporters as he left West Ham's training ground, Bilic - who was appointed in the summer of 2015 - said: "There are no hard feelings. I can be very proud of my work here.
"We didn't start this crucial season well. As in many clubs across Europe, the manager is the one who pays the price. It's a very logical move."
With 11 matches gone, he is the fourth Premier League manager to leave his job this season following Frank de Boer (Crystal Palace), Ronald Koeman (Everton) and Craig Shakespeare (Leicester).
A statement from joint chairmen David Sullivan and David Gold said Bilic had conducted himself with "honesty and integrity" and the decision to sack him had been made "with disappointment and heavy hearts".
"We see this as an exciting opportunity to appoint a quality manager to the position to inject fresh ideas, organisation and enthusiasm into a very talented squad," they said.
West Ham say Bilic's coaching assistants Nikola Jurcevic, Edin Terzic, Julian Dicks and Miljenko Rak have also left the club with immediate effect.
Chris Woods, who was goalkeeping coach under Moyes at Everton and United, is the only member of the coaching staff to remain.
A club statement said: "The search for a new manager to take West Ham United forward is under way and an announcement regarding Bilic's successor is expected to be made over the coming days,"
Former Croatia defender Bilic, 49, guided West Ham to seventh spot in his first season in charge, but an 11th-placed finish last term, their first at London Stadium, has been followed by a poor start this season.
The Hammers are 18th, having won just two Premier League matches in 2017-18 - and lost their first three league games of the campaign.
"We will now focus our entire efforts on bringing in the manager we believe can get the best out of the current squad of players and steer the club towards the top half of the table as quickly as possible," said Gold and Sullivan.
West Ham's next match is at Watford on Sunday, 19 November.