The Bavarians have not claimed a Bundesliga title at home since then, and they have yet to seal the title at the Allianz Arena, which was inaugurated in 2005.
This season started off poorly for Bayern as it lead to Ancelotti's sacking.
Bayern Munich have been crowned German Bundesliga champions for the 28th time in their history earlier today.
Sergio Cordova's shot was saved by Sven Ulreich, but bounced up into the face of Niklas Sule and rolled into the empty net, to make it 1-0.
Bayern have been incredibly impressive throughout this term, tasting defeat only three times across the entire campaign and possessing a vastly superior goal difference compared to anyone else in the league.
Robben all but sealed the title for Bayern after the hour-mark when he fired inside the right post after James kept the ball in play.
The Bavarian giants will formally lift the Bundesliga shield after the final matches on May 12. 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.
With five games left, Cologne are six points behind Mainz, who are 16th, which carries a relegation play-off berth against the third-best team in the second tier at the end of the season.
And the pressure proved too much for Augsburg in the 62nd minute as Robben, whose future at the club remains uncertain, hammered in a third after the hosts failed to clear Kimmich's cross.
Thorgan Hazard came off the bench to score twice as Borussia Moenchengladbach climbed to eighth with a 2-1 win at home to Hertha Berlin.