Achraf Hakimi, playing against his former club, gave PSG an early lead and Doue went from provider to finisher as his deflected shot doubled their advantage in the 20th minute.
Doue scored again just after the hour mark, ending any doubt about the outcome before Khvicha Kvaratskhelia ran away to get the fourth and substitute Senny Mayulu made it five.
Inter were simply no match for the French club, who recorded the biggest victory by any team in the final in the 70-year history of the European Cup and Champions League.
“This means everything. It’s my dream, it’s our dream. It’s incredible. The result is not by magic. I’m happy we did it like this, we’re now going to celebrate,” said Portuguese midfielder Vitinha, who was one of PSG’s creative sparks.
The triumph for the Parisians comes after more than a decade of huge investment from their Qatari owners, and five years after they lost to Bayern Munich in their only previous final appearance.
Already French league and cup double winners, they are remarkably just the second ever French winners of European football’s biggest prize — Marseille were the first in 1993, when they beat AC Milan in a final also played in Munich.
It is also a second Champions League for PSG coach Luis Enrique, who won with Lionel Messi’s Barcelona a decade ago.
This youthful PSG side is the best the competition has seen since, one that has been intelligently pieced together over the last two years and fully unleashed this season following the departure of Kylian Mbappe.
Indeed the star on the night was teenager Doue, who delivered a masterclass just before he turns 20 on Tuesday.
For Inter, there was to be no first Champions League title since 2010 as they failed to add to their three previous triumphs in the competition.
Simone Inzaghi’s side have now got to the final twice in three seasons and lost both, and this defeat comes a week after they missed out on the Serie A title to Napoli.
They end the campaign trophyless, and their ageing side will need to be rebuilt.
PSG gave their opponents no chance from the off on a sweaty night at the Allianz Arena, and they were ahead in the 12th minute.
It was a glorious goal, Vitinha threading a pass to Doue who squared for Hakimi to finish into an empty net, before refusing to celebrate against his former club.
It was also the earliest goal in a Champions League final since 2019, and recent history was already firmly against Inter.
The last final in which both teams scored was in 2018, while the last team to concede the first goal but still win were Real Madrid in 2014.
But soon Inter were further behind with a goal that came on a counterattack.
Willian Pacho prevented Inter from winning a corner, his clearance falling to Kvaratskhelia, who released Ousmane Dembele. His pass found Doue, and the youngster who was preferred in the starting line-up to Bradley Barcola fired past Yann Sommer, via a deflection off Federico Dimarco.
Inter only really came close to scoring in the first half when Marcus Thuram headed just wide at a corner, but things got worse after the break.
The night for Inzaghi’s side was summed up by defender Yann Bisseck, who came on for Benjamin Pavard early in the second half but limped off less than 10 minutes later.
Their back line was at sixes and sevens as PSG made it 3-0 on 63 minutes, Dembele’s flick releasing Vitinha before the little Portuguese playmaker set up Doue to beat Sommer at his near post.
Doue came off shortly after to rapturous applause, but his teammates were far from done.
Dembele sent Kvaratskhelia away to to make it 4-0 in the 73rd minute, and the 19-year-old Mayulu then played a one-two with Barcola before lashing in the fifth on 86 minutes.
That rounded off an incredible night, with PSG becoming the first team to score five goals in the final since Benfica in 1962. (AFP)
