He is believed to have cost Juve 1m for the loan and another 5m to make the move permanent.
"It is certainly a great feeling and I am very happy. The year could not have got off to a better start," Peluso told the official Juventus website.
"I will enjoy this splendid moment and hope to have many more. These have been the best months of my career and enabled me to arrive at Juventus. This is a dream come true.
"I think all the hard work in the smaller sides has helped me a great deal, as I earned everything I've got and hope to put my experience on to the field.
"I already know what awaits me with Antonio Conte. I always leave the pitch aware I've given my all. In today's football it is important to know how to play in many different roles. I started out as a full-back, but do not have a preferred position.
"I thank all the fans who wrote to me and hope to repay their faith with my performances."