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.
“The club’s 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,” added the statement.
Former Croatia defender Bilic, 49, was appointed in the summer of 2015 and guided West Ham to seventh place 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 have won just two Premier League matches in 2017-18 – and lost their first three league matches of the campaign.
Speaking after the defeat by Liverpool, Bilic told BBC Sport: “The pressure mounts game by game and at this moment it is big.
“I don’t feel a broken man. On the other hand, the situation for West Ham is not good and the club is above every individual.
“I cannot say anything negative [about the owners]. They have been supportive, very good to me in my two and a half seasons, but the situation is very difficult.”
West Ham’s next match is at Watford on Sunday, 19 November.
Is Moyes the man for Hammers?
BBC Sport understands West Ham held talks with former Everton and Manchester United manager David Moyes while Bilic’s future was being reviewed.
Speaking to Bein Sports on Sunday, the Scot denied there had been contact, but said he wanted to return to club management and was “interested” in the West Ham job.
Moyes said: “I’ve always said I want to go back into club management. If the right opportunity comes around, I’ll be interested.”
Asked specifically about West Ham, the 54-year-old said: “I am interested but at the moment that vacancy has not become available. I know what Slaven must be going through.”
Alan Irvine, Moyes’ former assistant at Everton, could be a candidate to join the Scot should he get the job.
Bilic – a success or a failure?
Bilic – who previously managed his country for six years – spent a reported £42m on players in the summer. That included the signings of forward Marko Arnautovic from Stoke City for a club record £20m, and former Manchester United striker Javier Hernandez from Bayer Leverkusen for £16m.
However, his side have taken just nine points from 11 league matches, conceding 23 goals in the process.
They endured a poor start to last season, too, winning just two of the first seven Premier League home games after moving into London Stadium, and suffering heavy defeats by Watford (4-2), Southampton (3-0) and Arsenal (5-1).
However, Bilic eventually guided the club to a mid-table finish and his record compares favourably with his predecessors, with none having claimed more Premier League points per game.
What do the fans say?
Graeme Howlett, editor of the West Ham fans’ website Knees Up Mother Brown
There’s a general consensus that Slaven Bilic’s time was up, even among those who have supported him throughout his tenure at the club.
The fans seem quite unanimous in that they are not particularly keen to see Moyes come in. They would prefer to see someone more progressive.
I suspect there would be an awful lot of criticism for the board, who are already under intense pressure following the move to the Olympic Stadium, which has not gone down well.
Various reasons have been mentioned, including his record at Sunderland, where he came in at a similar position and failed to keep them in the Premier League. There was also the incident with the female reporter which has been mentioned a few times.
Are West Ham fans ever truly happy? I don’t know. I saw Guus Hiddink mentioned on Twitter. Whether that’s the sort of calibre of manager we could attract, I’m not convinced.
It would have to be someone from that top tier to give West Ham fans some sort of confidence we can survive and stay in the Premier League next season.