"It's a special moment, because we now know we're champions", said Ribery, who has now won the Bundesliga eight times since joining in 2007.
Bayern's Bavarian neighbours Augsburg, though, were out to spoil the party and took an early lead through a freakish own-goal from defender Niklas Sule after 18 minutes. "He's not only a great coach but also a great person".
"It was clear that we'd be German champions at some stage with the lead that we had, but at the time (assistant) Peter Hermann and I returned it wasn't foreseeable as we were five points behind and the team wasn't really functioning properly", said Heynckes, the oldest coach to win a Bundesliga title at 72.
With one eye on Wednesday's Champions League quarterfinal second leg against Sevilla, in which Munich holds a slender 2-1 lead, coach Jupp Heynckes gambled by resting his stars.
"But we have to do it first ourselves and nothing is given away in the Bundesliga".
Top scorer Robert Lewandowski, plus Thomas Mueller, Thiago Alcantara, Mats Hummels and Javi Martinez all started on the bench.
Sevilla would have been encouraged by the comedy of errors in Bayern's defence that led to Augsburg's opening goal. Sergio Cordova forced Jerome Boateng to lose possession and Sven Ulreich then saved the Venezuelan forward's shot before the ball rebounded in off Niklas Suele's face. Bayern equalised out of the blue when Tolisso was left unmarked to head in from Joshua Kimmich's cross in the 32nd minute and the Bavarians took the game by the scruff of the neck.
The Bavarian giants will formally lift the Bundesliga shield after the final day on May 12.
Wolfsburg have ended their nine-game winless run after beating Freiburg 2-0 on Daniel Didavi's brace and bottom side Cologne were unable to defend their one goal advantage as relegation threatened Mainz reap a 1-1 draw by courtesy on Pablo De Blasis' equalizer. He added a second with seven minutes remaining.
Elsewhere, Borussia Monchengladbach bounced back 2-1 as two second-half goals from Thorgan Hazard cancelled out Hertha Berlin's opener through Salomon Kalou.