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 soccer'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."
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.
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 Mueller was denied by Julio Cesar at the start of the second half and pacy Dutch winger Arjen Robben also failed with an attempt to bring the scores level.
Inter had also gone close to more goals, especially from Sneijder just before halftime, but they were denied by some excellent goalkeeping from Butt.
With one end of the stadium decked out in the red of Bayern and the other filled with blue-and-black clad Inter fans, both teams made a cautious start on a balmy Madrid evening.
The build-up was dominated by the coaching duel between Van Gaal and his one time Barcelona assistant Mourinho but almost from kick-off it was clear both coaches had given the same instructions to their team -- go for goals.
Mourinho opted for a three-man attack of Samuel Eto'o, Goran Pandev and Milito while Van Gaal, without suspended playmaker Franck Ribery, trusted his attack to Ivica Olic and Thomas Mueller with Hamit Altintop and Robben providing the ammunition.
Inter's attempts obviously proved more fruitful but even before Milito put them ahead, their attack looked sharper and they always seemed the more likely to gain the early advantage.
Eto'o and Milito were a constant threat to the Bayern defence, while Olic and Mueller ultimately made little impression even though Robben toiled hard on the right wing and provided them with several opportunities.
Fears the game might turn into a sterile, defensive affair were unfounded and Inter, who won the European Cup in 1964 and 1965, claimed a long overdue third crown with a performance of passion, skill and rugged flair.
Their display was typified by excellent skipper Javier Zanetti who will never forget his 700th match for the club.
Mourinho will also never forget what might be his last match in charge of Inter as he followed Ernst Happel and Ottmar Hitzfeld as the only coaches to win the European Cup with two different sides following his success with Porto in 2004.
