Suarez joined the club from Ajax in January 2011 and has been a controversial figure at Anfield, serving two long-term bans - the first for racially abusing Patrice Evra, the second for biting Branislav Ivanovic.
And last summer Suarez suggested the club had reneged on an agreement to let him leave if they failed to qualify for the Champions League.
He missed the first six games of this season as he served a suspension for biting Chelsea's Ivanovic but he has been in sensational form since.
The striker says the support he has received from Liverpool fans was one of the main reasons for extending his contract, which will make him the highest paid player in the club's history.
"I am delighted to have agreed a new deal with Liverpool and have my future secured for the long term," Suarez told the club's website.
"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.
"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.
"We have a special relationship; they have love for me and in return I love them back. I will always do my best for them and hopefully we can achieve success together."
Liverpool manager Brendan Rodgers admitted the new deal was a huge boost for the club.
"This is fantastic news for everyone associated with the club; the team, the owners and most importantly the supporters," he said.
"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."
Principal owner John W Henry said the new deal proves Liverpool are progressing on and off the pitch.
"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," he said.
"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 said: "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."