Del Vecchio and Caltagirone oppose the proposed reappointment of Generali CEO Philippe Donnet in a challenge to the insurer's single biggest shareholder Mediobanca, people with knowledge of the matter have said.
In quitting the board, both criticised the steps followed by the insurer to renew the board, whose mandate expires in April.
Pucci, an independent board member, in September had voted against a resolution by Generali's board to file a slate of new board nominees for shareholders to vote upon in the spring - including Donnet as CEO.
In December, however, she backed Donnet's strategic plan, which was rejected instead by Caltagirone.
Following a query by Caltagirone, Italy's market regulator Consob on Friday concluded a review of Generali's board nomination procedure, deeming it legitimate.
(Reporting by Gianluca Semeraro; editing by Valentina Za)