The former Bolton, Newcastle and Blackburn boss has agreed a two-year contract at Upton Park.
Allardyce said: 'It is an honour to be the new manager of West Ham United. It is a fantastic club with a great tradition and loyal supporters who deserve to be in the Premier League.
Back in the game: Sam Allardyce will attempt to restore West Ham's Premier League status
'I can't wait to begin pre-season training as I am determined to get this club back where it belongs.'I wouldn't have taken this job if I didn't think we could bounce straight back into the Premier League. More than that, I wouldn't have contemplated the job if I didn't think there was the opportunity to build something substantial at West Ham.'
Sportsmail exclusively revealed Hammers co-owners David Gold and David Sullivan's move for Allardyce on Saturday morning.
His advisors spent Tuesday thrashing out terms over the move to Upton Park, which includes a substantial bonus for promotion.
Allardyce added: ''There is a core of very talented young players at the club who've come up through the youth system, have West Ham in their blood and who I know I can build a successful team around.
Double act: West Ham's co-owners David Gold and David Sullivan have moved swiftly to replace Avram Grant
'That's what I'm looking forward to, managing a club that wins more games than it loses and competing at the top of the table. We need to create a winning mentality and give the fans a team they can be proud to watch.
'I know there will be West Ham fans asking whether I'm going to abandon the style of play that's been the club's heritage over the years. All I'll say is it will be a tale of home and away.
'At Upton Park we'll attempt to play the kind of passing game the fans want. We will aim to continue in the same way on our travels but we'll also be tough, hard to beat and utterly resilient.'
Allardyce's appointment brings to an end the club's two-week search for a new manager after Avram Grant was sacked following relegation to the Championship.
Martin O'Neill, Alex McLeish, Neil Warnock and Dave Jones were all serious contenders for the role.
Friends reunited: Neil McDonald will be named as Allardyce's No 2 at Upton Park
Allardyce has been out of work since his shock sacking by Blackburn last December.
The Hammers' new boss has confirmed he will bring his former Ewood Park No 2 Neil McDonald with him to East London.
Allardyce admits he is unlikely to be able to prevent an exodus of the club's best players.
Goalkeeper Robert Green, striker Carlton Cole and player of the year Scott Parker are all expected to quit Upton Park over the summer.
'That's probably going to be the case for financial reasons,' Allardyce told talkSPORT. 'When a club is relegated it's a massive loss of revenue and you have to adjust.
'But for me, whatever happens, the basis is there of a very good squad and some good young players.'
On the future of England midfielder Parker, he added: "I don't know yet, we'll have to wait and see. From a distance it looks very difficult, but there is no indication of any bids for Scott yet.'
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Explore more:People: Martin O'Neill, Neil Warnock, David Gold, Alex McLeish, Sam Allardyce, David Sullivan, Robert Green, Carlton Cole Places: Newcastle, Bolton, London, United Kingdom