The 26-year-old’s previous deal was set to expire at the end of the season.
The new deal will keep the former Hibernian star at Celtic until the summer of 2015, with the option of a further year.
“I am absolutely delighted to sign this new contract with Celtic and commit my future to the club,” he told the club’s official website.
“I’m pleased that this is now all sorted and now I just want to get on with the job in hand.”
The Scotland international added: “I’m happy to be back from injury and I now want to just concentrate on the challenges which face us this season domestically and in Europe as we try to bring our fans some success.
“I would like to thank our supporters for the great backing they have given the club during the course of the season already.
“As always, they have been magnificent and I know the manager and all the players are totally focused on doing everything we can to achieve as much as we possibly can this season for our fans.”
Celtic boss Neil Lennon said: “Scott is a crucial member of our squad and someone we felt it was very important to keep at the club.
“He is a special player and his commitment, drive and all-round ability is something we feel is very important to us.”
“I’m pleased we’ve been able to finalise this and I would like to thank Scott’s representatives for their assistance in bringing these negotiations to a successful conclusion.”
