Gerrard had been linked with a move away from the Merseysiders following the club’s failure to qualify for the Champions League.
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However, following the arrival of fellow England midfielder Joe Cole, Gerrard is now looking forward to the new season under Roy Hodgson.
"It is a great signing for us. I know Joe well through the England setup and have seen first hand just how good a player he is," Gerrard said in the Liverpool Daily Post.
"He has proved his ability over many years in the Premier League - sometimes against us - so it will be fantastic to play alongside him in a red shirt for Liverpool.
"I've told him what a great club this is and I'm sure Joe's the sort of exciting talent our fans will love to see. I made it clear that I simply needed to concentrate on the World Cup and then have a decent holiday with my family.
"I wanted the chance to meet Roy Hodgson privately and having done so, I'm very impressed with his plans for the future."
Real Madrid, who’s new manager Jose Mourinho is a long-time admirer of Gerrard, last week distanced themselves from a move for the England vice-captain.
"Kaka will stay at Real, but the president does not agree with Gerrard because he is 30 and Perez doesn't want to know," Ernesto Bronzetti told GR Parlamento.
"Plus, Liverpool asked for €70 million."
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