The Uruguayan has been in stunning form for the Reds recently, after a turbulent summer in which he suggested the club had reneged on an agreement to sell him if they failed to qualify for the Champions League.
It had been expected that talks would continue throughout the season and the received wisdom was that the player would want to wait and see whether the Reds secured a Champions League place for next season, but the club on Friday confirmed he had signed a new deal.
Suarez told the club's official website www.liverpoolfc.tv: "Without doubt the backing I have received from the Liverpool fans has influenced my decision. I am so proud to represent them and go out to do my best for them every time I pull on the shirt."
Liverpool did not specify the length of Suarez's new deal but it is expected to make the 26-year-old striker the best-paid player in the club's history.
Suarez's spell at Anfield has often been a controversial one after being handed two long-term bans, one for racially abusing Manchester United's Patrice Evra and last season for biting Chelsea's Branislav Ivanovic.
Suarez added: "I am delighted to have agreed a new deal with Liverpool and have my future secured for the long term.
"We have some great players and the team is growing and improving all the time. I believe I can achieve the ambitions of winning trophies and playing at the very highest level with Liverpool. My aim is to help get us there as quickly as possible."
Liverpool manager Brendan Rodgers said Suarez had yet to reach his peak.
He added: "This is fantastic news for everyone associated with the club; the team, the owners and most importantly the supporters.
"Luis is a world-class talent and securing his services is crucial for what we are trying to achieve here.
"What's most important and most exciting is that, at just 26 years old, his best years are still ahead of him and we now know we'll be seeing him reach that potential in a Liverpool shirt."
Liverpool had to fend off interest from Arsenal in the summer, who had a bid of £40,000,001 rejected, but their determination to keep Suarez has paid off with the Reds now second in the Premier League with the Uruguayan the leading scorer in the top flight with 17 goals, four ahead of his nearest rival.
The club's principal owner John W Henry said: "We are committed to working hard to keep our best players and this is an indication that we are moving in the right direction and moving at a pace that impresses one of the best players in world football.
"The club has made major strides forward in recent years and we are all committed to delivering the success our supporters want and deserve."
Liverpool chairman Tom Werner added: "This demonstrates our commitment, as an ownership group, to building a team that competes at the highest level both in the Barclays Premier League and in Europe.
"Our primary motive is to do what is best for Liverpool Football Club and today's news is another significant step forward on this journey."