The victory ended Atlético's dreams of a historic double after they claimed the Spanish league title recently.
Gareth Bale, Marcelo and Cristiano Ronaldo hit the extra-time goals as Real Madrid came from behind to beat city rivals Atletico.
Although it was Real's 10th European Cup triumph, they had been staring at defeat at one stage against the La Liga champions.
Uruguayan defender Diego Godin headed Atletico in front in the 36th minute after a terrible blunder by Real goalkeeper Iker Casillas.
But Sergio Ramos headed in a Real leveller three minutes into second-half injury time.
Bale had squandered three good scoring chances for Real in the 90 minutes of regulation time before he struck in the 110th minute.
Marcelo added the third with two minutes remaining and Ronaldo the fourth from the penalty spot in the dying moments.