Despite dominating possession, the Bavarians struggled to create many meaningful chances in the first half with Stuttgart holding their defensive shape well.
However, after a goalless first half, Kane burst to life in the second period with a second-half hat-trick to win another trophy for Bayern.
In the 55th minute, he got on the end of a Michael Olise cross to head Bayern into the lead.
His second came with 10 minutes left on the clock, receiving a pass from Luis Diaz before turning well on the ball to spin past his marker and slotting home.
The England star completed his hat-trick two minutes into stoppage time at the end of the game, converting from the penalty spot after Olise was fouled in the box.
It was Kane's third triple in consecutive games after he also bagged a hat-trick in Bayern's final Bundesliga match of the season against FC Koln.
Kane ended the season with an incredible 61 goals in 51 games in all competitions for Bayern Munich.
It is the 21st time the Bavarians have won the German Cup but the first time they have done so since the 2019-20 season.
The result leaves Bayern as the most dominant team in Germany once again after a successful couple of years rebuilding under head coach Vincent Kompany.
FC Bayern Munich coach Vincent Kompany has said his side are determined to bring the DFB-Pokal trophy back to Bavaria when they face VfB Stuttgart in Saturday's final at the Olympiastadion Berlin.
Manuel Neuer will miss Bayern Munich's DFB-Pokal final against VfB Stuttgart on Saturday after failing to recover in time from a calf injury.
England manager Thomas Tuchel has made a ruthless call in his first major tournament squad, leaving out several high-profile names as he named his 26-man group for the 2026 World Cup.
Chelsea duo Mamadou Sarr and Nicolas Jackson have both been included in the Senegal squad for the upcoming 2026 World Cup, underlining their growing importance at international level.
