Owners David Sullivan and David Gold have turned to the former Bolton, Newcastle and Blackburn boss after considering Chris Hughton.
Sam Allardyce: "It's a fantastic club with a great tradition and loyal supporters.
"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.
"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 try to play the kind of 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."