The Hammers slipped to a 4-1 defeat against Liverpool on Saturday as they finished the weekend in the relegation zone.
“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,” read a statement on the club’s website.
Moyes has not managed since leaving relegated Sunderland at the end of last season, but used a TV appearance to signal his interest in the job.
“I’m interested, yes,” he told beINSPORTS.
“I’ve had no contact from West Ham but I’ve always said I want to go back into club management. If the right opportunity comes around, I’d be interested.”
The Hammers hierarchy wanted Bilic, the man they appointed in June 2015, to stay until the end of the season and see out his three-year contract.
But the manner of Saturday’s latest capitulation at the London Stadium, coming just a fortnight after an equally desperate 3-0 home loss to newly promoted Brighton, has forced the board to consider drastic action.