The new long-term deal will keep the highly-rated midfielder at Anfield until the summer of 2015.
“We are delighted,” said Liverpool boss Kenny Dalglish.
“He is a smashing lad to have around the football club but he hasn’t been signed for that, he has been signed because of what he does on the pitch.
“Certainly since I came in he has been a great asset to the team and has done tremendously well.
“He’s got wee Pedro to look after and now a new contract as well, and we’re delighted for him because he’s a really honest, genuine fella and that’s reflected in the way he plays.
“He’s happy to be here and play for the club and he’s getting everything that he deserves at the moment – including being a fixture in the Brazilian team – because of what he’s done on the pitch.”
Liverpool director of football Damien Comolli added: “I am very, very pleased. We have been talking for a few months now, ever since I arrived at the club.
“One of the first things I did after I arrived was to look at the contract situation and to see where Lucas was at. I knew we had to do something quickly because we couldn’t afford to lose him and didn’t want to lose him.
“If you look at his playing record he started 46 games last year in all competitions and this year it will be between 45 and 50. He is exactly what we want. He has the right mentality, quality and attitude.
“He understands what this club is all about and even though the discussions went on for quite a long time he always said to me ‘I want to stay and we need to find a solution’.
“Considering his performances on the pitch with us and with Brazil, and his attitude around the place – off the pitch he’s a great professional, totally committed and dedicated and it’s always team first when you speak to Lucas – that’s why we wanted him to stay.
“The celebration at Sunderland with the players after he’d had his baby shows that the other players were very happy for him and shows he is a team player.
“He could have gone to many clubs because he is highly rated around Europe, but he always said he wanted to play for Liverpool.”
