Downing, 29, has signed a four-year contract with the east London club and follows striker Andy Carroll in moving from Liverpool to Upton Park.
"I'm very excited. It's a great opportunity for me being here, it's a great club and I'm really excited to get going," Downing told the club's official website.
"I'm ready and I'm fit for the first game against Cardiff City (on Saturday). I've played a decent few games for Liverpool in pre-season, so there will be no problems on that front."
Downing becomes West Ham manager Sam Allardyce's fifth new signing of the close season, after Carroll, Romania captain Razvan Rat, Spanish goalkeeper Adrian and midfielder Danny Whitehead.