Crowned champions for the first time in April, goals from Victor Boniface and Robert Andrich put Leverkusen -- who play the Europa League final against Atalanta and the German Cup final this week -- on course for victory.
"Totally deserved. It was our goal after winning the title against Bremen. Very proud of the team – very satisfied and very happy," said Leverkusen coach Xabi Alonso.
"We can enjoy it just a little bit – and recover tomorrow."
Elsewhere on the final day of the league campaign, Cologne were relegated after a 4-1 loss at Heidenheim.
Union Berlin scored in stoppage time against Freiburg to win 2-1 and beat the drop, leapfrogging Bochum who will play a two-legged relegation play-off against second-division Fortuna Duesseldorf after losing 4-1 at Werder Bremen.
Leverkusen took the lead after 12 minutes when Amine Adli forced Augsburg goalkeeper Tomas Koubek into an error, winning possession before squaring for Boniface to tap in from close range.
Midfield star Andrich doubled Leverkusen's lead, backheeling in a rebound after 27 minutes.
Augsburg teenager Mert Komor pulled one back on his first start for the visitors with a stunning strike on the 62nd-minute mark, but Leverkusen held on to win ahead of what could be an historic week.
At the other end of the table, Union -- who were playing in the Champions League against the likes of Real Madrid as recently as December -- were locked 1-1 at home to Freiburg in stoppage time and headed for a relegation playoff clash with Duesseldorf.
Union had been reduced to 10 men when Michael Gspurning was red carded with four minutes remaining but won a penalty just into stoppage time.
Kevin Volland missed the spotkick but Janik Haberer was there to turn in the rebound and save Berlin.
Bochum, who looked to have secured top-division football with a 4-3 win at Union Berlin two weeks ago, will now need to beat Duesseldorf in a home and away playoff.
The loser will join relegated Cologne and Darmstadt in the second division.
Bayern's 'series of large mistakes'
Serhou Guirassy scored a brace as Stuttgart won 4-0 at home against Borussia Moenchengladbach, leapfrogging Bayern Munich, who lost 4-2 to a Andrej Kramaric-inspired Hoffenheim, into second spot.
Despite being without the injured Harry Kane, Bayern were 2-0 up after just six minutes thanks to goals from Mathys Tel and Alphonso Davies.
Maximilian Beier, selected as part of Germany's Euros squad on Thursday, cut the deficit two minutes later, capitalising on an error by goalkeeper Manuel Neuer to make it 2-1.
Kramaric then scored three goals in 20 minutes to turn the match on its head.
Bayern finished outside the top two for the first time since 2010-11.
"We made a series of a large, individual mistakes and gave the game away. We brought the opponent into the game, defended absolutely inadequately and gave up a 2-0 lead," outgoing manager Thomas Tuchel said.
"This has happened to us far too often."
Borussia Dortmund veteran Marco Reus signed off in impressive style in his last home match, scoring a goal and laying on another in a 4-0 win over Darmstadt.
In Dortmund's last competitive outing before June's Champions League final with Real Madrid at Wembley, Reus set up Ian Maatsen for the opener after 30 minutes, then added one of his own from a free kick eight minutes later.
Julian Brandt and Donyell Malen added second-half goals to seal the win.
Eintracht Frankfurt came from two goals down to draw 2-2 at home with RB Leipzig, while Mainz came from behind to win 3-1 at Wolfsburg.
