The Azzurri talent made the move from Villarreal on Friday for a reported €9m plus performance-related bonuses.
“We are happy to have brought a great talent like Rossi back to Italy,” said Viola patron Della Valle.
“It is not just a moment of joy for our fans, but a gift we wrapped up for all of Italian football.
“This move is also an important one that works within our project, which continues solidly. Rossi is one of the few talents still in circulation.”