The Uruguay forward was on international duty at the Olympics, but penned the new contract after returning to pre-season training with Liverpool.
Suarez has scored 21 goals in 52 appearances since moving from Ajax to Anfield in January 2011.
"To sign a new contract with Liverpool is unbelievable for me because I am so happy here at both the club and also in the city," said Suarez, who is believed to have extended his stay at the club until 2016.
"That is important for me and I am very happy with my new contract.
"When you are a kid, everybody wants to play for Liverpool. I am here now and it is a dream for me, and now I am a Liverpool fan.
"I am happy off the pitch because the people of Liverpool are good with me and my family. I try my best on the pitch and when you are happy off the pitch, you are happy on the pitch.
"I want to say thank-you to the fans because they are our 12th player. The supporters of Liverpool are unbelievable.
"Five or six years ago I watched on TV the stadium and the club, and now I play here and the supporters have helped me. That's very important for me."
Liverpool manager Brendan Rodgers said: "I'm delighted. When you have the opportunity to work with world-class players it's fantastic.
"There were certainly a few clubs who were interested in him but over the off-season he and I communicated well - and he's committed himself for the long term here now.
"He's really looking forward to playing in this way of working. As a manager and for the supporters, I'm delighted because I know how important he is for them."
Liverpool club's official television channel had earlier sparked confusion when it appeared to announce that Suarez has signed a new contract, only for the broadcast to be cut off with no other confirmation forthcoming.
During a 60-second news bulletin on LFC TV on Tuesday afternoon, the station claimed that the Uruguay striker had signed a new "long-term" deal amid speculation of interest from Serie A champions Juventus.
However, the broadcast was cut short before the end of the report, and no further word had come out from the club either from the channel or its press office.