The Buccellati family, who in 1919 founded the jeweller famous for its ornate, lace-like creations, will retain a 15 percent stake.
A source familiar with the deal said the acquisition gave Buccellati an enterprise value of 270 million euros (230.31 million pounds) or 6.6 times its revenues.
The source said Clessidra had not been able to reach an accord with Cartier owner Richemont <CFR.VX> after discussing a possible sale of a controlling stake in Buccellati to the Swiss group.
Clessidra, which recently changed hands and is now owned by Italy's Pesenti family following the death of its founder, bought a 67 percent stake in Buccellati in 2013.
It said Buccellati's revenues had risen 60 percent since then.
Mediobanca advised Clessidra and Buccellati on the deal.
(Reporting by Valentina Za and Massimo Gaia; Editing by Adrian Croft)