He exclusively told Goal that: "Milan and I have come to an agreement based on the opportunities that will be afforded me in the first team.
"And Brescia have been after me for the past two months so I am glad to be joining them.
"I know that I have to play regularly to secure a place in the Super Eagles which has informed this decision."
The Super Eagles winger scored a hat-trick at the Confederations Cup against Tahiti and that feat compelled Milan to give him the No.90 jersey.
But the 23-year-old would have been fourth choice behind Stephan El Shaarawy, M'baye Niang and Mario Balotelli.
Oduamadi spent last season on loan at Serie B side, Varese, for whom he scored two goals.