The 30-year-old Argentine scored after 35 and 70 minutes to seal a deserved victory for Inter at the Santiago Bernabeu stadium and complete an unprecedented treble for a Serie A club following their Italian league and Cup double.
It was also a personal triumph for Inter's masterful coach Jose Mourinho who etched his name alongside football's great club managers by becoming only the third man to win the European Cup with two clubs.
But the Portuguese, linked with a move to Real Madrid, has been considering his future and after the match told reporters:
"It's more probable that I will go than I will stay. We deserved this competition not just for this match but for the path we took. Inter did exactly what I wanted."
EXCELLENT FOOTBALL
Beaten Bayern boss Louis van Gaal, whose team missed out on winning the first German treble, said the better team had won.
"Inter played excellent football tonight and what we did wasn't enough. They deserved to win."
World Cup-bound Milito, who had spent much of his career as a journeyman striker, has reached the heights this season with 22 goals in his first Serie A campaign for Inter.
He scored the goal that clinched the domestic title last weekend, got the winner in the Italian Cup final and sent the Inter fans wild in Madrid with a clinically-taken opening goal that set them on their way to their latest triumph.
"It's a joy I've never experienced. It's incredible. I am so happy for Inter because we wanted this so badly. We are so happy and it's a unique sensation," Milito told reporters before surprisingly being coy about whether he will stay at the club.
"Let's see," he said before joining the celebrations which lasted for almost an hour after Inter received the cup from UEFA president Michel Platini, whose idea to switch the final from a Wednesday to a Saturday was rewarded with a memorable occasion.
He said he wanted more children at one of Europe's great showpiece occasions and the kids of the Inter players were still playing with the gold celebration bunting on the pitch until way past their bedtimes as their dads celebrated victory.
The disconsolate Bayern players, who had already won a league and cup double, could only ponder what might have been.
FIRST GOAL
Milito set Inter on their way when he nodded goalkeeper Julio Cesar's long punt down to Wesley Sneijder, ran on to the Dutchman's pinpoint through ball and shimmied to make space before lifting a shot into the net over Hans Joerg-Butt.
His second was also superbly taken leaving Bayern defender Daniel Van Buyten bamboozled and beaten before firing past Butt into the far corner of the net.
Before the decisive second strike, which came after English referee Howard Webb played the advantage during the build-up, Bayern twice came close to an equaliser.
Striker Thomas Muller was
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