كتب : Sherif Tarek
The Nerazzurri became the first Italian team to complete a treble of trophies, having won the Serie A and Coppa Italia earlier.
Portuguese tactician Mourinho, who has just finished his second season with Inter, was highly praised for the Italian giants' unprecedented feat.
Inter last won the Champions League in 1965.
Mourinho is tipped to end his tenure at San Siro very soon to take charge of Real Madrid.
Joy
Argentine international Milito hit both goals either side of the interval to help his team snatch the prestigious title.
He opened the scoring five minutes past the half-hour mark when he combined with Wesley Sneijder to lose his maker Daniel van Buyten and go one-on-one with the keeper before slotting home.
Milito doubled Inter's lead on 70 minutes after he neatly finished off a counter attack. The 30-year-old dribbled past Buyten to dink an easy goal from inside the area.
"I have never felt joy like this in my life. Inter wanted this so much for the President, who deserves it and is the ultimate fan," he said after scoring both goals in the 2-0 victory over Bayern Munich.
"This is football. I always tried to learn everything, even though I am 30 years old," said the former Genoa and Real Zaragoza striker.
"We all deserve this celebration, the club and the President. I hope to remain next season and I thank Inter for wanting me last summer.
"I am happy right now, but we will have to wait and see what happens."
The match's goals: