France winger Ousmane Dembele and Spain midfielder Fabian Ruiz scored for PSG in the first half.
Lyon defender Jake O'Brien got a consolation goal in the second half.
PSG won the league and cup for the first time since 2020 when they achieved a domestic treble by also lifting the now defunct League Cup.
Mbappé celebrated with a big roar after the final whistle. With an equally big smile on his face, he hugged and high-fived his teammates. The ecstatic PSG staff lifted Mbappé and threw him in the air.
"You feel a bit more the weight of things because you realise that it's really over," Mbappé told broadcaster beIN Sports.
"When I said goodbye to the Parc des Princes, there were still some games left, so you are still focused on what awaits you. Now, I have nothing left with PSG. But I'm very happy to have been able to finish with a trophy."
Despite losing in the final, Lyon still qualified for the Europa League by finishing sixth in the league. They were bottom of the league in December but racked up more points than any other club in the second half of the season.
Dembélé opened the scoring in the 22nd minute by heading home a cross from Nuno Mendes.
Ruiz doubled the lead by converting a rebound in the 34th after his header was blocked by O'Brien.
Lyon goalkeeper Lucas Perri pulled off some outstanding saves in the opening minutes, denying Bradley Barcola and Warren Zaire-Emery, but misjudged the flight of the ball when Mendes made the cross for the opener.
O'Brien cut the deficit to 2-1 by heading in a corner in the 55th.
Mbappé tried hard to find the net in his last outing for PSG. A curling shot from the edge of the box didn't trouble Perri in the 20th and he volleyed over the bar in the 41st.
In seven seasons with PSG, Mbappe has won 15 trophies, including four French Cups.
Although Mbappe did not add to his tally, he leaves as PSG's all-time top scorer in all competitions with 256 in 308 appearances.
"I'm happy to have been part of its history and to have made it a bit," Mbappé said.
The French Cup final was marred by violence as Lyon and PSG supporters clashed on a highway leading to the venue a few hours before kickoff.
Supporters threw flares and windows were smashed on buses full of supporters. Some buses were set on fire.
The match was relocated to Stade Pierre Mauroy in the north of France because of preparations for the Olympic Games.
Villeneuve d'Ascq became the first city outside the Greater Paris area to host the French Cup final since the competition's inception in 1917.
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