Rodgers, who was widely praised for leading the Reds to the brink of a first league title in 24 years last season, had been set to enter the final year of his contract this summer.
But the Northern Irishman revealed he would hold talks with the club about an extension at the end of the campaign, and Liverpool has moved swiftly to tie him down for the long term.
"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."