The Bavarians clinched a 26th German league crown, and their first silverware of the season, thanks to two goals from top scorer Robert Lewandowski in the first half.
Four days after their away-goals defeat by Atletico Madrid ensured a third consecutive Champions League semi-final exit, Bayern went eight points clear of second-placed Borussia Dortmund who lost 1-0 at struggling Eintracht Frankfurt.
"A big compliment to everyone in the team. I am happy to have lived these experiences here," said Bayern coach Pep Guardiola who will join Manchester City at the end of the season.
"I want to share this title with (predecessor) Jupp Heynckes. We achieved something very special, four league titles in a row."
Heynckes started the run during the 2012-13 treble-winning season before Spaniard Guardiola took over.
Bayern can secure the double when they meet Dortmund in the German Cup final on May 21 in Berlin.
The final whistle sparked a party at the 15,000-seater Audi Sportpark, with forward Thomas Mueller grabbing a loudhailer to lead singing with the fans.
In Guardiola's penultimate league game after three seasons in charge, Bayern went ahead when Lewandowski scored from the penalty spot in the 15th minute.
The visitors took their foot off the gas and let Ingolstadt back into the game with a 42nd-minute penalty converted by Moritz Hartmann.
BAYERN CONSISTENCY
"It is no small feat to win the league four times in a row," said Mueller. "It required a lot of work, quality is not enough if you don't put the work into it.
"The consistency we have shown in the last few years is incredible. The beer glasses will be in full swing this evening."
Borussia Moenchengladbach's Andre Hahn scored twice in a 2-1 comeback victory over Bayer Leverkusen that all but secured fourth place and a Champions League qualifying round spot.
Gladbach, who lost their opening five league matches of the season, have 52 points. Mainz 05, Hertha Berlin and Schalke 04 are all on 49.
Schalke conceded an 89th-minute equaliser in their 1-1 home draw with Augsburg while Hertha slumped to a 2-1 defeat against Darmstadt 98.
Sandro Wagner's 83rd-minute winner delighted Darmstadt and made sure of their Bundesliga status next season.
Former champions Werder Bremen drew 0-0 at Cologne and now meet Eintracht in their last game of the regular season.
Werder are in the relegation playoff spot on 35 points with Eintracht one place above on 36. VfB Stuttgart, champions in 2007, are second from bottom on 33 after a 3-1 defeat by Mainz 05.
(Editing by Toby Davis and Tony Jimenez)
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