Suarez, whose original deal was set to expire in 2016, will reportedly earn around £160,000 until the end of this season and then £200,000 per week over the final four years of the contract.
The striker, who is the Premier League's top scorer with 17 goals from 11 outings this season, has become the highest-paid player in Liverpool's history.
"I am delighted to have agreed a new deal with Liverpool and have my future secured for the long term," said Suarez.
"We have some great players and the team is growing and improving all the time," he told the club's official website. "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."
Suarez joined Liverpool from Ajax for £22 million in January 2011. He pens a new deal after a summer when it seemed he would leave the club for Champions League football at Arsenal or Real Madrid, but Liverpool refused to authorise his sale.
"This is fantastic news for everyone associated with the club; the team, the owners and most importantly the supporters," said manager Rodgers.
"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."
Club owner John W Henry owner echoed the sentiments of Rodgers after completing a significant piece of business for the club in securing a player who seemed so unsettled in the summer.
"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," said Henry.
"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."