Allardyce, 56, was installed as the Hammers' new manager yesterday, with the club's owners turning to the former Blackburn Rovers coach to guide them back to England's top tier after they were relegated to the Championship following a poor campaign.
"It's a fantastic club with a great tradition and loyal supporters," Allardyce told the club's website. "I am determined to get this club back up.
"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."
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.
Allardyce, who recently held talks with Pro League club Al Jazira about replacing Abel Braga, who will return home to Brazil in the summer, has been out of work since his surprise sacking by Blackburn in December.
Michael Owen has penned a new one-year contract to keep him at champions Manchester United for a third year.
Owen's present two-season deal was about to expire and, having been overshadowed by Javier Hernandez last season and knowing new signings were expected - in addition to the return of Danny Welbeck from Sunderland, it was anticipated the former England striker would be released.
However, Ferguson evidently still views the 31 year old as an important member of his squad.
"I am delighted Michael is staying for a further year and we will look to give him more opportunities in the new season."
Mario Balotelli, the Manchester City striker, has been sent home from Italy's training camp with a right knee injury.
He had to be helped off the pitch after sustaining the injury during a training match against Italy's Under 18 side yesterday.
Balotelli will now miss both tomorrow's 2012 European Championship qualifier against Estonia and Tuesday's friendly with Republic of Ireland.
Newly-promoted clubs Queens Park Rangers and Norwich City have started an early summer clear-out, with eight players leaving QPR and Norwich deciding against offering new contracts to Matt Gill, Jens Berthel Askou and Sam Habergham.
Pascal Chimbonda, Gavin Mahon, Georgias Tofas lead the departures as Rangers prepare for life in the top flight next season.