Real won their 10th European Cup - and first since 2002 - after coming within a whisker of losing following Diego Godin's 36th-minute opener.
Sergio Ramos powered home a headed equaliser in the third minute of added time to force extra time before goals from Gareth Bale and substitute Marcelo and a penalty from Cristiano Ronaldo won the game.
Real's victory means Ancelotti joins legendary Liverpool boss Bob Paisley as the only managers to win three European Cups - having twice guided AC Milan to the silverware - while he has also won the trophy twice as a player.
The delighted Italian said: "We have done it with a lot of suffering and difficulty, but in the end we have done it and we deserved it.
"I am very happy for this because we have won a trophy that for Real Madrid is very important. We have worked hard all year for this."
Ramos was equally delighted to notch the equaliser, saying: "It is the most important goal I have scored.
"It is an incredible feeling. We kept fighting until the end for the fans.
"It is not my goal, but one for all Madrid fans, my family and all those that have supported us until the end. We deserved it after so many years."