Downing has agreed a four-year deal with the Hammers and he follows Andy Carroll in making a permanent move from Anfield to Upton Park this summer.
The 29-year-old midfielder, who has won 34 caps for England, is West Ham's fifth new recruit of the summer following the signings of Carroll, Romania captain Razvan Rat, Spanish goalkeeper Adrian and midfielder Danny Whitehead.
Downing is ready to compete for a place in the West Ham side to face Cardiff on Saturday on the opening weekend of the Barclays Premier League season.
"I'm very excited," said Downing, who is predominantly a left winger but spent a lot of time playing at left back for Liverpool last season.
He added on West Ham's official website: "It's a great opportunity for me being here, it's a great club and I'm really excited to get going.
"I'm ready and I'm fit for the first game against Cardiff City. I've played a decent few games for Liverpool in pre-season, so there will be no problems on that front."
Liverpool have taken a significant loss in selling Carroll, who spent last season on loan at Upton Park, and Downing to West Ham for a combined fee reported to be around £21million.
Kenny Dalglish signed both players for Liverpool in 2011, with Carroll reported to have cost £35million from Newcastle and Downing £20million from Aston Villa.
But neither featured in Brendan Rogers' long-term plans and Downing was told last autumn that he could leave the club.
Downing responded by forcing his way back into the Liverpool first team and he made a total of 45 appearances last season, featuring both on the left wing and at left back.
Carroll welcomed Downing's signing for West Ham, Tweeting: "Great signing for us today [Tuesday]! #cantwaittobeback #bargain"