Xabi Alonso's side entered the clash with Bremen off the back of seven straight victories in all competitions, including a 2-0 triumph in the first leg of their Europa League quarter-final with West Ham United on Thursday.
Leverkusen had posted nine straight league successes ahead of the match, meanwhile, with their last dropped points coming in a goalless draw with Borussia Monchengladbach on January 27.
A historic campaign could bring two more trophies, as the German giants will face Kaiserslautern in the DFB Pokal final at the end of next month, while they are in a strong position to progress to the final four of the Europa League.
Leverkusen have won the Bundesliga title with five games to spare, which will allow head coach Alonso to rest key players as the team also battle for success in Europe.
The Black and Reds have previously been runners-up in the Bundesliga on five previous occasions, with their last second-placed finish coming in 2010-11.
Leverkusen have finished fifth, fourth, fifth, sixth, third and sixth in their last six campaigns in Germany's top flight, but they have now secured the biggest prize on offer in impressive fashion.
There had been huge speculation surrounding Alonso's future as head coach, with both Liverpool and Bayern Munich believed to be keen to appoint him this summer.
However, the Spaniard recently committed his future to Leverkusen, and the Black and Reds will start next season as the defending champions, with Bayern's recent dominance coming to an end.
Bayern last failed to win the Bundesliga title in 2011-12, when Borussia Dortmund lifted the trophy, and Thomas Tuchel's side are now locked in a battle with Stuttgart for second.
Leverkusen took the lead against Bremen from the penalty spot in the 25th minute, with Victor Boniface finding the back of the net after Jonas Hofman had been fouled by Julian Malatini.
Amine Adli rattled the crossbar late in the first period, with the hosts looking for a second, but just the one goal separated the two teams at the half-time break.
Leverkusen doubled their advantage in the 60th minute courtesy of a 25-yarder from Granit Xhaka, before Florian Wirtz netted a third eight minutes later with an equally impressive strike.
Wirtz netted his second to make it 4-0 in the 83rd minute, which led to a pitch invasion, but the play eventually resumed once the fans had left the field, and the attacker completed his hat-trick in the final stages to cap a sensational title success for the home team.
Alonso's side will now switch their attention back to the Europa League, preparing to head to West Ham for the second leg of their quarter-final, before returning to league action next Sunday.