It is believed the Hammers have paid an initial fee of £1.5million plus an extra £4million in performance based add-ons.
Downing joins the Hammers following two frustrating years at Anfield following his £20million move from Aston Villa in 2011. The 29-year-old England international went on to make 65 Premier League appearances for the Reds, scoring three goals.
Downing, who has signed a four-year contract, told whufc.com: “I’m very excited. It’s a great opportunity for me being here. It’s a great club and I can’t wait 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.
“It’s all happened quickly, but I’m really excited and hoping to play a part on Saturday.”
The former Middlesbrough and Aston Villa player has been capped 34 times by England.
Downing will wear the No.23 shirt for the Hammers.