The designer is set to present his first collection for Rochas in Paris in February 2014, reported Vogue.
"I'm excited about this collaboration. Rochas is synonymous with French sophistication and a couture spirit, and as a designer I could not ask for anything more inspiring," Dell'Acqua said.
"Working for a maison with such a historical heritage is a rare opportunity and I feel grateful it was given to me," he added.
According to the fashion house, Zanini is making a departure as a result of a "mutual decision".
"As an iconic French maison, Rochas has been an endless source of inspiration for me. I learned a lot over the past five years and I feel fortunate to have been part of such a wonderful adventure," he added.