"It is a sign of the continued interest of the Berlusconi family who have always been close to the club and offered economic support," Milan chief executive Adriano Galliani told reporters.
"The fact that the club president's brother (Paolo) and one of his daughters are on the board is a good sign which must also be welcomed by fans as an act of faith."
Barbara, 26, has been touring departments of the club for the last year to get used to the organisation and has been the subject of vast Italian press coverage speculating about her relationship with Milan's Brazil striker Alexandre Pato.
The Italian football federation also said in a statement on Wednesday that Milan forward Zlatan Ibrahimovic's appeal against his three-game Serie A ban for swearing at a linesman had been rejected.
