Jupp Henyckes' side went into the game needing to match or better Borussia Dortmund's result against Augsburg and Bastian Schweinsteiger's second-half strike was all they needed to seal all three points.
The Bavarians have topped the table since the opening day of the season, and have wrapped up the league crown earlier than any other team in history, beating their own record of matchday 30 by two matches.
"I'm extremely delighted of course. It's a very emotional moment," Heynckes told Sky.
"I told my players in the briefing that my first title as a player was the most emotional moment in my career.
"We have nine players in the squad who secured their first Bundesliga. It was extremely difficult to perform today after the tough encounter against Juventus.
"But the players fought hard and were certainly a little bit lucky to have won the game at the end of the day."
|"My first title as a player was the most emotional moment in my career. We have nine players who secured their first Bundesliga"
- Jupp Heynckes
Captain Philipp Lahm added: "We've been talking about the championship for a long time and we're very happy to have finally secured it.
"Today, we were eager to win and continue our streak, winning the consecutive 11th match of the second half of the season.
"Of course we will open a few bottles of beer today, but we also have to set our sights on the next challenges. On Wednesday, we want to reach the next round of the Champions League.
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|Schweinsteiger strike seals 23rd Bundesliga title|
"If you look at the statistics, we work better defensively now and played a lot of matches to nil. Furthermore, we had a good run with winning a lot of important matches.
"At the end, we deservedly top the Bundesliga table."
Jupp Heynckes' side have set a host of records en route to the title, including the number of away wins, while they are on course to smash Dortmund's record points total of 81 set last year.
They need just two wins from their remaining five games to beat their own best-ever tally of 25 victories in a season, and are currently beating the highest-ever goal difference of 64, which they themselves achieved in 1972-73.
Due to their ongoing commitments in the Champions League and the DFB-Pokal, Bayern's management have delayed any celebrations until their final home game of the season, against Augsburg on May 11.