The Argentina international striker hit both goals in the 2-0 win over Bayern Munich.
"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.
Milito has been absolutely decisive in the last few weeks, netting the only goals in the Coppa Italia Final over Roma, the 1-0 win over Siena that decided the Scudetto and the Champions League Final against Bayern Munich.
"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."