The Italy international won the Champions League with AC Milan on Wednesday.
Oddo said: “I want to dedicate this award to my team-mates and my coach but also to my former club and my former team-mates.
“I made a choice six months ago to join Milan in the hope of playing at the top level in Europe and have the possibility to win titles.
“It wasn’t an easy decision but now I can say that I made the right move by joining Milan.”