The 26-year-old, who has been capped by England 27 times, becomes Kenny Dalglish's fourth summer signing following the arrivals of Jordan Henderson from Sunderland, Blackpool's Charlie Adam and Roma goalkeeper Alexander Doni.
"It's a great feeling and I'm very happy to be here. It's been a long time coming and I've had to wait a few weeks, but I'm really pleased to be here," he told www.liverpoolfc.tv.
"With the tradition, the manager and the players they have here, there was a big temptation to come here and once I knew of their interest, there was only one place I wanted to go.
"It will be a great feeling to run out at Anfield. It's always nice to come and play here. The atmosphere is always great and the fans are brilliant.
"When I wanted to come to Liverpool, it was the first thing I thought of - playing at Anfield in front of those great fans. I'm really looking forward to it."
Downing's arrival marked the end of a busy day for Liverpool, who also completed the signing of Doni.
The 31-year-old Brazilian is thought to have joined on a free transfer after agreeing personal terms and passing a medical.
Liverpool director of football Damien Comolli said: "We are delighted to sign Doni. It's a position we felt we had to strengthen because it will allow our young goalkeepers to go on loan and get some experience at some point during the season, which is crucial in their development."
Doni, who has 10 caps for his country, will provide back-up and competition for Liverpool number one Jose Reina - a role he also played at Roma behind Julio Sergio.