The Rossoneri released a statement on Tuesday confirming Braida "leaves the club today - he was a precious collaborator for a very long time, characterised by prestigious results that must also be attributed to his important work."
It is a huge break, as Braida has been at Milanello for 27 years in various capacities.
His exit is the sign of a new era opening up under Barbara Berlusconi, who became joint-CEO with Adriano Galliani this month.
Braida has been linked with future jobs at other football clubs, including Sampdoria and Monaco.
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