The 56-year-old, whose last managerial post was at Blackburn Rovers before he was fired last December, succeeds the sacked Avram Grant and pledged to instil "a winning mentality" at the east London club who finished bottom of the table this season.
"I wouldn't have taken this job if I didn't think we could bounce straight back into the Premier League," Allardyce said on the club's website.
"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."
Whatever he builds, though, may be without several of the current players with Allardyce saying it will be hard to keep hold of the likes of Footballer of the Year Scott Parker.
"There will probably be an exodus of top players for financial reasons," Allardyce told talkSPORT radio. "There's a dramatic loss of revenue, even with the parachute payments, and you have to adjust, like every club does.
"I don't know if I'll be able to keep Parker. We'll have to wait and see but it looks like it will be difficult."
Other players who could leave the club are England goalkeeper Robert Green and England striker Carlton Cole.
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"Whatever happens with some of the big players there's the basis of a good squad and some very, very good young players to rebuild quickly," added Allardyce.
West Ham's move to London's Olympic Stadium for the 2014/15 season is a major incentive for promotion back to England's top flight and in Allardyce they have gone for one of the domestic game's most established names to mastermind that push.
A no-nonsense centre-back in his playing days, Allardyce managed Blackpool and Notts County before spending eight successful years at Bolton Wanderers from 1999, getting the team promoted and establishing them as a Premier League side.
He moved to Newcastle United in 2007 but lasted less than a season and joined Blackburn in December 2008 before he was sacked two years later after the arrival of new Indian owners.
Often criticised for his long-ball style, Allardyce said he would not sacrifice West Ham's traditions but it would be "a tale of home and away".
"At Upton Park, we'll attempt to play the kind of passing game the fans want," he said. "We will aim to continue in the same way on our travels but we'll also be tough, hard to beat and utterly resilient."
