Del Vecchio's holding company Delfin said in a statement it had appointed Milleri, who is the CEO and chairman of eyewear giant EssilorLuxottica, as chairman.
Delfin added that Chief Executive Romolo Bardin, another Del Vecchio lieutenant, would continue in his role.
Delfin's main asset is a 32% stake in EssilorLuxottica, worth more than 20 billion euros.
The Luxembourg-based firm is also the single biggest shareholder in Milanese merchant bank Mediobanca with 19.4% and the second-biggest investor in Italian insurer Generali with 9.8%.
It owns a 27% stake in Paris-listed Covivio and is a long-time investor in bank UniCredit with a 2% stake.
($1 = 0.9591 euros)
(Reporting by Claudia Cristoferi, writing by Giulia Segreti; editing by Valentina Za)