Arsenal defender Gabriel Magalhaes fired the last of his team's penalties over the bar to hand PSG a 4-3 shootout victory at the Puskas Arena on Saturday.
The nervy game was poised at 1-1 at the end of regulation time and extra-time, sending the game to spot-kicks.
Arsenal had led after six minutes when Kai Havertz broke away and blasted past PSG goalkeeper Matvey Safonov.
But the defending champions dominated possession and Ousmane Dembélé levelled from the penalty spot in the 65th to take the final to extra time for the first time in 10 years.
Eberechi Eze also missed an earlier spot kick, but David Raya saved from Nuno Mendes to let Arsenal stay level.
Lucas Beraldo scored the last of PSG's spot kicks, meaning Gabriel had to convert to take it to sudden death.
But he blasted high over the bar to spark celebrations from PSG players and fans inside Puskas Arena.
"It's incredible,"PSG captain Marquinhos said.
"From the very first day of this season, the coach said it's hard to win, and winning twice is even more difficult. So we all had to get back to work. That was the mentality."
The French giants are only the second team to retain the trophy in the modern era after all-time kings of Europe Real Madrid.
Luis Enrique became a three-time winner as a coach and has moulded a team that is simply too good even for the best the continent has to offer.
That includes an Arsenal team that won the English Premier League last week and topped the first stage of the Champions League with a perfect winning record, finishing 10 points and 10 places ahead of PSG.
That mattered little in the Hungarian capital as PSG reaffirmed their status as the dominant force in European soccer.
"It's even more special because we knew before the match how difficult it would be," Enrique said.
"I think it's deserved over the course of the whole season, even if the final was very closely contested."
After demolishing Inter Milan 5-0 in last year's final, PSG endured a tougher foe as Arsenal sat deep and relied on the best defence in the competition.
By going back to back, Luis Enrique has achieved what his good friend Pep Guardiola could not after winning Champions Leagues at Barcelona and Manchester City.
He also joined Carlo Ancelotti, Guardiola, Bob Paisley and Zinedine Zidane in an elite group of coaches with at least three European Cups.
The next target will be to emulate Madrid's three in a row under Zidane from 2016-18.
"We were able to carry the game to Arsenal, dominate, and I am so happy because if I analyse the whole season we clearly deserve the trophy," Enrique said.
And with a starting lineup in Budapest with an average age of under 24, Enrique has built a team that has the potential to dominate for years.
Having waited 22 years to get their hands back on the Premier League trophy, Arsenal's wait in Europe goes on.
This was their 226th game in the European Cup or Champions League without lifting the trophy. No other team has played so many without being champions.
"First of all you have to go through that pain, digest it and then turn it into fuel and improve and reach a different level because it will demand a different level with the quality that is around Europe," manager Mikel Arteta said.
"I want to congratulate PSG, Luis (Enrique) in particular, because they are, in my opinion, the best team in the world."
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