Leading 1-0 from the first leg in Paris last month, Eric Maxim Choupo-Moting put Bayern in front on the night at the Allianz Arena and substitute Serge Gnabry wrapped up the victory a minute from time.
Bayern were worthy winners against a flat PSG side, for whom neither Kylian Mbappe nor Lionel Messi had the expected impact on the game while Neymar was missing with an ankle injury.
It is the second season running in which PSG have gone out of the Champions League in the last 16, and the fifth time in the last seven campaigns the Qatar-owned club have failed to go beyond the first knockout round.
They were not helped by injuries in defence, with captain Marquinhos forced off after 36 minutes with a rib problem and his replacement, Nordi Mukiele, also having to be substituted at half-time.
Vitinha might have put the French champions in front in the first half, but Matthijs de Ligt cleared his attempt off the line.
Bayern went ahead just after the hour mark, Leon Goretzka setting up the unmarked Choupo-Moting for an easy finish after Marco Verratti had been dispossessed in his own box.
Sergio Ramos came closest to getting the visitors back into the game before Gnabry clinched Bayern's victory late on.