The result means Bayern are German league champions for the 28th time in their history, and it was the sixth year in a row they have won the Bundesliga since their treble-winning season in 2013.
Augsburg took a shock lead through an own goal by Niklas Suele, but the Bavarians roared back as Corentin Tolisso, James — who then assisted Arjen Robben — and Sandro Wagner all scored.
The result leaves Bayern 20 points clear with five league games left and underlined their absolute dominance of the Bundesliga.
“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. “Nothing is given away in the Bundesliga.”
Following the match, the 34-year-old Robben revealed he is considering offers from other clubs despite winning the 11th league title of his career. Saturday's victory was Robben's seventh Bundesliga crown since joining Bayern in 2009, but with his contract expiring in June, he could yet leave at the end of the campaign.
“Other teams have contacted me,” Robben told Sky, having also won the Spanish and English league titles with Real Madrid and Chelsea respectively.
The Dutch winger implied he would not definitely sign a contract extension with Bayern even if offered one.
Turnaround after coach switch
Bayern were five points adrift when Carlo Ancelotti was sacked as head coach last September, but 72-year-old Jupp Heynckes who replaced him credited the players with turning Bayern's fortunes around.
“The coach is responsible for the big picture, but first and foremost the players are the protagonists, they have done an outstanding job,” said Heynckes.
With one eye on Wednesday's Champions League quarter-final second leg against Sevilla, in which Bayern hold a slender 2-1 lead, Heynckes gambled by resting his stars.
Top scorer Robert Lewandowski, plus Thomas Mueller, Thiago Alcantara, Mats Hummels and Javi Martinez all started on the bench in Augsburg.
Sevilla would have been encouraged by the comedy of errors in Bayern's defence that led to Augsburg's opening goal.
Jerome Boateng lingered over a back pass and Colombian forward Sergio Cordova robbed him of possession, sending Boateng tumbling to the turf.
Cordova's shot was blocked by Bayern goalkeeper Sven Ulreich, but the ball ricocheted up into Suele's face and into Bayern's goal to stun the visitors on 18 minutes.
However Munich hit back to lead 2-1 by half-time. Joshua Kimmich picked out the unmarked Tolisso to head them level on 32 minutes and Bayern then laid on a top-class goal to take the lead at the WWK Arena.
Kimmich was again involved, firing a pass across goal after combining with Robben for Juan Bernat, who backheeled the ball which James fired home seven minutes before the break.
The Colombian then ensured the title was heading to Munich, hooking the ball back into play at the far post for Robben to drill his shot inside the near post on 62 minutes.
Ribery celebrated his 35th birthday with a cameo appearance for the final eight minutes before Wagner headed in Bayern's fourth.
The Bavarian giants will formally lift the Bundesliga shield after the final matches on May 12.
By AFP's Ryland James