The 41-year-old, who inherited the Anfield hotseat in 2012, has been rewarded for guiding the club to second in the Premier League last season, which in turn saw the Reds qualify for the Champions League for the first time since 2009-10.
In a joint statement, owner John Henry and chairman Tom Werner said: "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."
Meanwhile, Rodgers added: "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.
"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 have won 54 of the 97 matches under Rodgers's management.