"It's always good (to win a title) - we knew it was going to happen, but we still had to confirm it", said Robben, who has now won the Bundesliga title seven times since joining Bayern in 2009.
Niklas Sule kicked off proceedings with an own-goal on 18 minutes before Corentin Tolisso (32'), James Rodriguez (38'), Arjen Robben (62') and Sandro Wagner (87') all weighed in with goals.
Heynckes will also be hoping to secure an incredible treble this season with the club still competing in both domestic competitions as well as on the European stage.
"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.
Fresh from wrapping up the Bundesliga title at the weekend, James Rodriguez and Bayern Munich will look to finish the job against Sevilla in the UEFA Champions League quarter-finals at the Allianz Arena on Wednesday (kick-off: 08:45 PM CEST/ 06:45 PM GMT/ 02:45 PM EST).
"But we have to do it first ourselves and nothing is given away in the Bundesliga". Defender Jerome Boateng, under no pressure, lost control of the ball and was dispossessed by Sergio Cordova leaving the Venezuelan with only Sven Ulreich to beat.
The Colombian then ensured the title was heading to Munich for their third.
Franck Ribery, also out of contract at the end of the season, marked his 35th birthday with a late cameo appearance off the bench.
The Bavarian giants will formally lift the Bundesliga shield after the final day on May 12.
Wolfsburg won 2-0 at Freiburg in a match between two sides just above the bottom three and fighting to stay up.
Cologne's chances of avoiding the drop took a blow after relegation rival Mainz came from behind to earn a 1-1 draw in their decisive clash. Jonas Hector gave Cologne an early lead but Pablo de Blasis levelled five minutes into the second half, leaving the Billy Goats six points adrift of safety in 17th place. Didavi added a second with seven minutes remaining.