The match finished 1-1 after normal and extra-time
Real Madrid have won the Champions League for the 11th time in their illustrious history.
But Zinedine Zidane's side needed penalties to achieve it at the San Siro.
After a 1-1 draw after full-time and extra-time, Juanfran missed his kick in an otherwise exemplary shootout display for both sides to allow Cristiano Ronaldo, who had been quiet after a fitness worries during the week and was fifth in line to take a kick for Real, to put in the winning penalty.
Real dominated the early stages of the game, fashioning the first chance of the game when a Casemiro flick on a Gareth Bale free-kick forced Atletico keeper Jan Oblak into a point-blank save.
But they did hit the front on 15 minutes when Sergio Ramos got the final touch - with more than a hint of offside - on a Toni Kroos free-kick which was touched on by Bale.
Real Madrid's Sergio Ramos celebrates after scoring the opening goal during the Champions League final soccer match between Real Madrid and Atletico Madrid at the San Siro stadium in Milan, Italy, Saturday, May 28, 2016. (AP Photo/Manu Fernandez)
Atletico grew into the game as the first half wore on but couldn't break through.
However, they had a great chance straight after half-time when Fernando Torres got across Pepe as a ball was fired into the box and fell under the challenge, leading referee Mark Clattenburg to award a penalty.
But Atletico's forward star of the season, Antoine Griezmann cracked his penalty against the crossbar to let Real in off the hook.
Atletico's Yannick Carrasco gets a kiss as he celebrates after scoring during the Champions League final soccer match between Real Madrid and Atletico Madrid at the San Siro stadium in Milan, Italy, Saturday, May 28, 2016. (AP Photo/Luca Bruno)
Ten minutes later, defender Stefan Savic fired wide from six yards out as Atletico began to create more openings.
With 11 minutes to go, Bale came close to making it 2-0 but he saw his shot cleared off the line.
They were made to pay for that shortly after as Atletico right back Juanfran got down the flank and pulled across goal which was smashed home by half-time substitute Yannick Ferreira Carrasco to make it 1-1, leading to extra-time.
But neither side could score leading to a penalty shootout.
Real Madrid's Cristiano Ronaldo scores the winning penalty in the shoot-out Picture by: Mike Egerton / EMPICS Sport
With penalties poised at 4-3 to Real, Atletico full-back Juanfran missed his kick, allowing Ronaldo to take the winning kick which he took with aplomb before removing his shirt in celebration.
It's the 11th time that Real have won the Champions League or European Cup and the first for Zidane as a manager, while it's third time unlucky for Atletico in the final of European club football's showpiece.