The former Udinese fullback was paraded before the local media yesterday.
He spent the last 18 months at Roma who co-owned his contract until earlier this month.
"I missed out on the Scudetto with Roma, now I want to win it with Juve," Motta said at his official unveiling.
"We have the same chances as all the other teams, Inter included.
"I felt good at Roma. I have left an extraordinary group of players. It hurts to have been so close to the Scudetto and not to have won anything.
"We lost the title against Sampdoria even if Inter allowed us to come back by slowing up their step.
"Now I want to achieve many successes with the black and white shirt."
Motta was then asked about his Torino past.
"Being an ex-Granata doesn't frighten me. I don't deny anything about my past. Torino was an important experience in my development, but now I have turned the page and I am very happy to be at Juve.
"I have a lot of work to do, a lot to improve and to show. It's a big chance. It will be up to me to repay the trust the club have put in me on the pitch."