"My time with Milan finished in the best possible way, with a goal in the final game, so it was all perfect," Inzaghi, 38, told Italian media.
"Now I begin another dream, which is to be a coach and hopefully win the Champions League."
Inzaghi, who scored 156 Serie A goals in 370 games, added: "I couldn't go to play elsewhere, as I could not just leave Milan. Today I received a proposal from England, but I can't leave Milan.
"I signed a two-year contract and will coach the youth team, then I hope one day to lead the senior squad too."
However there was widespread frustration when star striker Zlatan Ibrahimovic and key defender Thiago Silva were sold to Paris Saint-Germain, although Milan insisted money would be ploughed into new signings and reducing the club's debt.