Inzaghi is promoted from his primavera role to replace Clarence Seedorf.
Writing on his official website, he expressed his happiness at having made the step up.
"I'm very happy, today for me is an unforgettable day," Inzaghi said.
"I thank the President Berlusconi and the whole club for their confidence and the prestigious professional opportunity they have granted to me.
"I'm honoured and proud to be the Coach of a team that has been my life for so many years. It is a team and a club with which I have shared joy and unforgettable moments.
"I will give everything of myself for these colours, passion and determination, as I have always done both as a player and as Coach of the youth teams.
"A hug to all Rossoneri fans. Forza Milan!"
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