It has been a matter of when and not if Bayern regained the title from Borussia Dortmund for some weeks and Bastian Schweinsteiger's 53rd-minute effort gave the visitors the win they needed.
The afternoon could have been more comfortable for Bayern, with David Alaba sending a first-half penalty against a post, but they moved 20 points clear of Dortmund with only 18 left to play for.
The victory also ended a mini title drought as they won their first crown in three seasons.
It was not quite on the same level as the 9-2 thumping of Hamburg in their last league clash, but the Bavarian giants can now turn their attention to completing the treble. They are well-placed in their Champions League quarter-final with Juventus and in the last four of the DFB-Pokal.
Borussia Dortmund overturned a half-time deficit to secure a 4-2 home victory over Augsburg and consolidate second place in the Bundesliga standings on an afternoon which saw them officially dethroned as champions by Bayern Munich.
Dortmund went ahead after 22 minutes through Julian Schieber but found themselves behind at the interval after goals from Daniel Baier and Kevin Vogt stunned the hosts.
But Schieber restored parity by netting his second goal in the 52nd minute before Neven Subotic put Dortmund ahead in the 64th minute and then Robert Lewandowski sealed the triumph in stoppage time.
Leverkusen were held 1-1 by Wolfsburg, allowing Schalke to close the gap on the final automatic Champions League place to four points with a 2-0 win at Werder Bremen.
Andre Schurrle put Leverkusen in front after 13 minutes, but Simon Kjaer earned a point for the Wolves.
Schalke's win at Werder Bremen came courtesy of goals from Julian Draxler and Ciprian Marica.
Borussia Monchengladbach remained in the running for European football next season with an uninspiring 1-0 home win over 10-man Greuther Furth.
Luuk de Jong scored the only goal of the match in the 74th minute for Gladbach, eight minutes after Furth went a man down when Matthias Zimmermann was given a second yellow card.
Gladbach have lost just once in their last six matches to move to 41 points while last-placed Furth have not won in eight matches to remain on 15 points - nine points from the relegation play-off spot.
On Friday night Markus Gisdol celebrated a winning start to life as coach of Hoffenheim, who gained a much-needed survival boost with a comfortable 3-0 win over Fortuna Dusseldorf.
Roberto Firmino's early strike and an Andreas Lambertz own goal put the hosts on their way to victory before Kevin Volland sealed all three points for only the sixth time this season.