The Bavarians ended the two-year reign of Borussia Dortmund by clinching a 22nd Bundesliga title faster than any club in the league's 50-year history.
Bastian Schweinsteiger flicked the ball into the net with a neat backheel in the 52nd minute to lift Bayern to 75 points ahead of second-placed Dortmund, who beat Augsburg 4-2.
"It's a fantastic moment and I'm winning a league title after 23 years again," said coach Jupp Heynckes, who guided Bayern to the championship in 1989 and 1990 during his first stint as coach.
"I have won a few championships in my time as player and coach but never when it was still that cold," he said of the fastest title win in Bundesliga history.
"My players are now harvesting all the work they put in throughout the year. They put into action exactly what I told them."
But Germany international Schweinsteiger made sure of their 11th straight league win this year with his seventh goal of the campaign, turning in a superb Philipp Lahm cross after the full-back's burst down the right wing.
"You feel that this team wants more," said club boss Uli Hoeness. "Now we want to win the Champions League and the German Cup. There will be time to celebrate at some point."
"We really wanted to win this and get the title out of the way," said Bayern captain Lahm. "There will be one or two beers that will be opened on the way back tonight. But we now want to focus on Juventus. It [the season] is not finished yet."
Bayern's 23rd league title covers their 22 Bundesliga crowns and a German national championship trophy in 1932.
