The former Atalanta fullback turned his loan into an outright deal this week.
"We expected Juventus to take up their option to sign him," representative Beppe Bozzo told Tutto Juve.
"This move makes Federico very proud. It means that Peluso, in his first season at Juventus, was able to find an important place in the team.
"I can confirm that the boy is very happy. He wanted to stay at Juve and his wish has been granted.
"Juventus have great faith in Peluso and he is delighted that he can continue this experience in Bianconero."