Leading 5-4 after last week’s thrilling first leg in Paris, Luis Enrique’s side stretched their overall advantage early on through Ousmane Dembele.
Harry Kane struck in added time for Bayern but it was too late for a comeback.
PSG will be favourites against Premier League leaders Arsenal on May 30 in Budapest after an excellent defensive display at the Allianz Arena, also the scene of their maiden Champions League final triumph over Inter Milan last year.
The French giants are hoping to become only the second back-to-back winners since 1990, after Real Madrid.
Bayern were angered by some first-half refereeing decisions but were largely toothless in attack.
The six-time European champions have still not reached the final since beating PSG in the 2020 showpiece in Lisbon.
PSG extended their aggregate lead to two goals in just the third minute, as Dembele fired the ball into the roof of the net from Khvicha Kvaratskhelia’s cutback.
Manuel Neuer made fine second-half saves from Kvaratskhelia and Desire Doue to keep Bayern in the tie.
Kane drilled in his 14th goal in the competition this season in the fourth minute of injury time, but it was too little, too late for the home team.
