The 25-year-old's previous deal had been due to expire at the end of next season, and Southampton were linked with a move for the Australia international earlier this month.
However, Celtic have now secured the future of the midfielder, whose new contract will run until the summer of 2023.
"I feel great to have signed a new contract. I'm very proud and honoured to be able to commit my future to the club," Rogic told the club's official website.
"I enjoy playing regular football here. I'm working under a top-class manager and to play my club football here is something that's very special to me so I couldn't be happier to have signed a new contract.
"The support here is very special and sometimes it's hard to describe. To feel so loved and wanted by the fans is all a player can really ask for.
"It's my job and the players' job to repay that. Now that my future's sorted I can focus completely on playing football and giving everything I have for the club, as I have done for the past five years."
Rogic has scored eight times and registered nine assists in 40 appearances for Celtic this season.