Carlton Cole opened the scoring in the first half with a finely taken goal after Matt Taylor's lofted through ball, before Thomas Ince, levelled after half-time with a similar effort.
Ricardo Vaz Te then sealed the win with a goal in the last five minutes to send the jubilant West Ham fans wild.
The Hammers now join Southampton and Reading as the two other sides promoted to England’s top division, with the Royals going up as champions.
They will take the place of Wolves, Blackburn and Bolton in the top tier, and will hope to emulate last season’s three promoted sides, Swansea, Norwich and QPR in retaining their Premier League status.
The play-off final is said to be the match which earns the most money in the world of football, with promotion to the Premier League rumoured to be worth around £90 million.