The international fashion chain said the appointment was part of the process of separating the roles of shareholders and management within the business.
Before working at Warner Music, Caccia Dominioni held senior positions at Time Warner and Philips Italia. He will take up his position in June.
Previous Benetton group managing director Silvano Cassano quit the fashion retailer last November, along with finance director Pier Francesco Facchini, amid rumours of a boardroom rift. Facchini has been replaced by ex-Burberry chief finance officer Emilio Foa.
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