Rodgers, who was widely praised for leading the Reds to the brink of a first league title in 24 years last season, had been due to enter the final year of his contract this summer.
|6/1||Liverpool are 6/1 with William Hill to win the title next season|
"I am both humbled and privileged to be offered the chance to extend my stay at this great club. I am very happy to build on the foundations we have built over the last two years and now we move onto the next phase which I believe will be as exciting, challenging and rewarding," Rodgers told the club's official website.
"I would like to place on record my thanks to the players and staff, who have been absolutely brilliant for me since the day I started at this great football club. I am grateful to our owners and senior management team who have supported me and who share my vision of how we can progress on the field.
"Finally, I must thank the supporters who are at the heart of everything we do here. I am honoured every day to lead this team and I thank the fans for their continued support as together we strive to bring success back to Liverpool Football Club."
Liverpool owner John W. Henry and chairman Tom Werner added: "We are very fortunate to have a hugely talented individual leading our football performance and in whom we place our trust to deliver the vision we share for Liverpool Football Club.
"Brendan is at the heart of what we, as an ownership group, are trying to achieve on the pitch. This season has reaffirmed everyone's belief that we can bring football success to Liverpool and we are all committed to working together to achieve that.
"Players and supporters have made it clear how important Brendan is to our success and so to have him commit to us for the long term is a great boost for everyone going forward."