The gripping final ended 1-1 after extra time, with PSG becoming only the second club to successfully defend the Champions League since the competition was rebranded in 1992.
The French giants joined Real Madrid, who won three consecutive titles between 2016 and 2018, while also becoming the 10th club in European Cup history to claim back-to-back crowns.
Arsenal made a dream start and appeared poised to end their long wait for a first European Cup triumph. The Premier League champions, who ended a 22-year domestic title drought this season, struck early through Kai Havertz.
The opening goal came after PSG captain Marquinhos attempted a clearance that ricocheted off Arsenal winger Leandro Trossard.
The loose ball fell kindly for Havertz, who sprinted from near the halfway line before firing from a tight angle into the roof of the net.
The breakthrough carried echoes of Arsenal's only previous Champions League final appearance 20 years ago, when they also took an early lead. This time, however, PSG responded.
Arsenal's defence resisted pressure for nearly an hour before finally being breached in the second half. The turning point arrived when defender Cristhian Mosquera brought down Khvicha Kvaratskhelia inside the penalty area. Following a lengthy delay and VAR review, the referee pointed to the spot.
Ousmane Dembele calmly converted, sending goalkeeper David Raya the wrong way to level the score at 1-1.
With neither side able to find a winner in extra time, the contest became the first Champions League final in a decade to be decided by penalties.
PSG held their nerve, while Arsenal's hopes were shattered when Gabriel Magalhaes blasted the decisive spot-kick over the crossbar, handing the Parisians a historic triumph.
Paris Saint-Germain coach Luis Enrique joined an exclusive group of managers to win three European Cups after guiding the French champions to a dramatic penalty-shootout victory over Arsenal in the UEFA Champions League final on Saturday.
Gabriel Magalhaes said it was "painful" after missing the decisive penalty as Arsenal lost the Champions League final to Paris Saint-Germain in a shootout in Budapest.
Arsenal manager Mikel Arteta described Paris Saint-Germain as the best team in the world after watching his side suffer Champions League final heartbreak, but insisted the Gunners must respond with ambition in the transfer market.
Raheem Sterling has been arrested following a motorway incident after his Lamborghini collided with barriers on the M3, adding to a difficult period for the former England forward.
