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, 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.
"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."