The 24-year-old Coman ghosted in at the far post unchecked by the PSG defence and was ready to meet a cross from Joshua Kimmich in the 59th minute.
The singing PSG contingent around the directors’ box was silenced in a stadium that was largely empty due to coronavirus restrictions.
“It is extraordinary, a great joy,” Coman said. “I feel a bit sad for Paris. They’ve had an extraordinary journey. We must respect what Paris have done.
“We tried to put a lot of pressure on them.
“We didn’t concede a goal, that’s the most important thing. It was a great final.”
It completed an incredible transformation this season under Hansi Flick, who took charge in November with Bayern fourth in the Bundesliga.
The season is now over – three months later than planned due to the coronavirus pandemic pause in play – with Bayern treble winners.
The European Cup joins the Bundesliga trophy – won for an eighth successive season – and the German Cup.
Bayern join deposed champion Liverpool as six-time champions of Europe, behind only AC Milan (seven) and Real Madrid (13).
Coman’s strike punished PSG’s wastefulness in the first half as Neymar and Mbappe both failed to beat Bayern keeper Manuel Neuer from close range while Angel di Maria and Ander Herrera also narrowly missed the target.
PSG substitute Eric Maxim Choupo-Moting missed two late opportunities to level for the French side, who are still waiting to win their first Champions League title after billions of euros of investment from the Qatar royal family.