Rodgers was delighted to complete the deal and believes that it shows confidence in the vision he has for the club.
"It's great when one of your best players commits to the vision going forward. Daniel is a terrific player and I am absolutely delighted he has committed himself. It's a big boost for everyone connected with the club," said Rodgers.
"He's one of the best centre-backs in world football. His balance, his reading of the game, his defensive qualities and his ability to bring it out from the back is outstanding.
"He's in love with the club and the supporters, and I'm really looking forward to continuing to work with him."
Liverpool currently sit 14th in the Premier League table and will face Stoke City in their next match.