McDonald was only a year into his previous four-year contract, but such was his exploits last season, the club agreed to rip that up and make the striker a new five-year offer.
The player's agent, Lou Sticca, told tribalfootball.com: "It's a great credit to Scott and Celtic that this new agreement has been found.
"Celtic's decision to hand Scott a new contract is fantastic reward for his efforts last season - and also acknowledgement from the club of how much they think of him. We're all delighted."
Meanwhile, McDonald also told tribalfootball.com: "I'm very, very pleased.
"It's been an incredible year for me personally and to cap it off with a championship medal and this new contract is something that is simply beyond my dreams.
"The management and treatment I've received at Celtic is first class and just makes me more determined to repay the faith they have shown in me."