Victory for the German champion secures a lucrative treble after it also won the league and domestic cup earlier this year.
Despite all the attacking talent on display, one goal was enough to separate the two sides with former PSG man Kingsley Coman heading in the winning goal in the 59th minute.
Coman, a French international, guided his header into the bottom corner to add yet another trophy to his cabinet.
The 24-year-old has won the league title in every season he’s spent as a professional player, starting with PSG’s Ligue 1 victory in 2013.
Meanwhile, it’s yet more European disappointment for PSG which was playing in its first final.
The French champion, which was also bidding for a treble, has become obsessed with winning the Champions League since Qatar Sports Investments bought the Parisian club in 2011.
More than one billion dollars has been spent on the playing squad but stars such as Neymar and Kylian Mbappe were unable to get their side past a dominant Bayern which is still unbeaten in 2020.