Donnet, who has also been appointed managing director, will continue in his current role as country manager for Generali Italia, which he has held since July 2013.
He brings with him many years of international experience, having held senior management positions at a number of global insurance groups.
Donnet will also become chairman of the investment committee and executive director in charge of overseeing the group’s risk management control systems.
The role vacated by Greco had been filled by group chairman Gabriele Galateri di Genola on an interim basis.
The board also appointed Alberto Minali as general manager of the company, in addition to his current role as group chief finance officer.
In his new role, Minali will take on responsibility for finance, operations, insurance & reinsurance, marketing, strategy, and data.