Real Captain Sergio Ramos netted the first goal of the match after just 15 minutes at a packed San Siro. But the match reached the extra time stage when Yannick Carrasco came off the bench to level on 79 minutes.
The two periods of extra time went scoreless and the match was pushed into penalties stage. When defender Juanfran's effort blasted off the bottom of Keylor Navas's upright Ronaldo came to the front to secure the second trophy for Real in three years.
With this win, Real coach Zinedine Zidane has joined an elite club of players - including, notably, Johan Cruyff, Carlo Ancelotti and Pep Guardiola - to have also won the title as a coach.
Man-of-the-match Ramos said Zidane's arrival in January following the sacking of Rafael Benitez was "really important for us". "He has a great relationship with the players. We'll be celebrating this with him!" said Ramos.
Zidane was overjoyed at lifting European club football's biggest prize. "I was given the chance to come to this amazing club, and then to coach it. I have a phenomenal team and great players who are also talented, and it was together we achieved what we did tonight," said Zidane. Real last won the title in Lisbon.
Atletico coach Diego Simeone had pledged his side that will eventually win the Europe's premier competition. "We started the game badly," admitted Simeone. "I think I could start thinking about my future. It puts a lot of years on you," it added.