"The Chairmen and board of West Ham United would like to place on record their thanks and gratitude to Slaven and his team for their services over the past two-and-a-half years, but believe a change is now necessary in order for the Club to move forward positively and in line with their ambition," a club statement read.
"West Ham United can confirm that Bilic's coaching assistants Nikola Jurcevic, Edin Terzic, Julian Dicks and Miljenko Rak have also left the Club with immediate effect. The Club's search for a new manager to take West Ham United forward is underway and an announcement regarding Bilic's successor is expected to be made over the coming days."
Moyes, who has been without a job since resigning as Sunderland boss following their relegation from the Premier League last season, is the leading contender to take over at West Ham having been installed as the 1/20 favourite with the bookmakers.
Speaking at the weekend at the prospect of replacing Bilic at the London Stadium, he said: "I've always said I want to go back into club management. If the right opportunity comes around, I'll be interested.
A run of five straight defeats during the back-end of last season saw Bilic under pressure from the start of the 2017-18 campaign and he appeared to be on the brink after losing four of the club's opening six league games.
Victory over Tottenham Hotspur in the Carabao Cup was followed by a draw with Crystal Palace that gave Bilic a stay of execution but the thumping defeat to Liverpool – which led to droves of supporters leaving before the final whistle – has seen co-owners David Gold and David Sullivan take action.
The upcoming international break means West Ham are not back in competitive action until the trip to Watford on 19 November, which comes prior to the visit of Leicester City before a game at Moyes' former club Everton at the end of the month.
A joint-statement from Gold and Sullivan added: "Sadly, performances and results have not been of the expected standard and, in recent weeks, we have not seen enough indication of the required improvement to give us the encouragement that things would change and we would meet our Premier League aspirations this season.
"As custodians of the Football Club it is our responsibility as a Board to do what is best for West Ham United, and we believe a change is now necessary to ensure we can begin to move the team back in the right direction. 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."