The 18-year-old, who scored what proved to be the winner in the memorable victory over Barcelona last week, has agreed a contract which ties him to Parkhead until at least the end of the 2015/16 season.
The young striker has become a regular feature in Neil Lennon's first team since marking his senior debut with two goals in a 3-0 win over Motherwell in April.
Watt has found the target six times in his 14 appearances in all competitions this season, and he had no hesitation in extending his stay with the club.
"I'm delighted to have signed this new contract," he said. "I'm a Celtic fan and this is where I want to play my football.
"The last couple of weeks have been incredible, and to sign the contract just a week after scoring against Barcelona is brilliant.
"I know I've still got a lot of hard work ahead of me in my career, but it's great to know that I'll be here as part of this exciting young team the manager is building at Celtic."