Federico Valverde broke the deadlock from close range for the Champions League holders in the 59th minute after the Italian Europa League winners held their own in the first half.
Madrid began to rack up the chances and Mbappe rifled home in the 68th minute after Jude Bellingham spotted his dart into space in the box to seal the victory.
“It was a great night, I’d been waiting for this moment for a long time. To play with this shirt, with this badge, for these fans, it’s a gift for me.
“We won a trophy too, that’s very important, we know that here we always have to win and I am very happy,” Mbappe told Movistar, speaking in fluent Spanish.
Madrid’s triumph ensured coach Carlo Ancelotti equalled former Los Blancos coach Miguel Munoz on a joint-record 14 titles won at the helm of the club.
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