Moyes returns to the Premier League after taking Sunderland down last year.
He was in the running for the Scotland job but has taken over at West Ham as they look to avoid relegation after sliding into the bottom three.
Moyes replaces Bilic and it is understood his contract is until the end of the season.
Stuart Pearce is expected to be named as his assistant and he will take training today as he bids to get to the know the players.
Moyes has called on the fans to support the team – after the board was stunned by the reaction to his appointment when it was still being finalised.
In a video posted on Twitter Moyes said: “I’m really looking forward to meeting the supporters. Being in the stadium with them.
“I’m looking forward to seeing them getting right behind the team and my team also.
“We need the support, we need everybody with us, it’s a big job we have in hand now but I’m sure with everybody together we can get the right results between now and the end of the season.”
He will have bridges to build with the fans who are concerned by his appointment after relegation with Sunderland and poor spells in Spain and with Manchester United.
And with chief executive Karren Brady, who criticised him for sexist comments made to a reporter last season.
“If it’s wrong to be a bit racist, it’s also wrong to be a bit sexist,” Brady wrote at the time in her column for the Sun.
“But while he should keep his job, I really hope that from now on he starts to think before he speaks.”
Joint-Chairman David Sullivan, however, is delighted to bring the Scot to the London Stadium and believes he can get the Hammers out of the rut.
He said: “I would like to welcome David to West Ham United.
“This is a unique position for David Gold and myself – it is the first time in almost eight years at West Ham United that we have appointed a new manager during the season.
“We need somebody with experience, knowledge of the Premier League and the players in it, and we believe David is the right man to turn things around and get the best out of the players at the Club. He is highly regarded and respected within the game, and will bring fresh ideas, organisation and enthusiasm.
“He proved with Everton that he has great qualities and we feel that West Ham United is a Club that will give David the platform to display those qualities again.”
West Ham sacked Bilic yesterday after a poor start to the season sees them third bottom in the Premier League.
He went following the defeat to Liverpool on Sunday with the chairmen claiming they had a duty to do what was best for the club.
“During the summer, the Board invested heavily signing the players Slaven believed would complete the squad he needed to push the Club back towards the level we had reached in his first season, and we believe we have the players capable of doing that,” a message from Sullivan and David Gold read.
“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.”
