Liverpool ended two points behind champions Manchester City after faltering near the end of the season, but are looking forward to a return to the Champions League for the first time since the 2009-10 season.
In a joint statement, owner John Henry and chairman Tom Werner said Rodgers was the right manager to bring silverware back to Anfield.
"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."
Rodgers's second season in charge at Anfield saw a dramatic improvement on his first when they finished seventh.
"I am both humbled and privileged to be offered the chance to extend my stay at this great club," he said.
"I am very happy to build on the foundations we have built over the last two years and now we move on to the next phase which I believe will be as exciting, challenging and rewarding."
(Reporting by Martyn Herman; Editing by Robert Woodward)
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