Ancelotti was sacked by Bayern at the end of September following a 3-0 Champions League defeat to Paris Saint-Germain. Or, put differently, they have been champions more times since 1985 than every other club in Europe's big five leagues barring Barcelona, Juventus and Real Madrid in their entire history.
A beaming Heynckes, who took over from Carlo Ancelotti with the club not performing at its best earlier this campaign, also had praise for the former manager. They are through to the German Cup semi-final and, on Wednesday, host Seville in the Champions... Celebrations were relatively muted as the side looked to the remaining targets.
"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.
Augsburg took a shock lead through an own goal by Niklas Suele, but Bayern roared back as Corentin Tolisso, James Rodriguez, Arjen Robben and Sandro Wagner all scored.
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Meine herzlichen Glückwünsche an die Bayern, seine Spieler, an den Klub, seine Fans und an meinem Freund Jupp Heynckes // My congratulations go to Bayern, their players, the club, the fans and my friend Heynckes.
The result leaves Bayern 20 points clear with five league games left and underlined its absolute dominance of the Bundesliga. "Everyone delivered great work".
Sevilla would have been encouraged by the comedy of errors in Bayern's defence that led to Augsburg's goal. "This title is also for him", he added. Cordova's shot was blocked by the Bayern goalkeeper but ricocheted off the hapless Suele's face and into the net. "He is a great coach", Bayern's head coach Jupp Heynckes said.
Robben all but sealed the title after the hour-mark when he fired inside the right post after James kept the ball in play. Elsewhere, Bruno Labbadia claimed his first win since taking over at VfL Wolfsburg when they beat Freiburg 2-0 away with two goals from Daniel Didavi.
An early goal by Cologne's Germany defender Jonas Hector was cancelled out as Pablo De Blasis headed an equaliser for Mainz five minutes into the second half.