The Spain Under-21 international had been well regarded in Madrid and made 35 La Liga appearances over the previous two campaigns, but after only accumulating eight starts during that period he opted to leave Carlo Ancelotti's side.
Morata, 21, netted eight times in La Liga last term as Real finished third behind Atletico Madrid and Barcelona and, although never a regular starter, Juve will pay €20 million for his services over three years.
Despite leaving the reigning European champions, Morata is certain he made the right choice in moving to Turin and he feels being surrounded by the likes of Andrea Pirlo, Gianluigi Buffon and Arturo Vidal will only inspire him further.
He told reporters: "I've wanted to play at Juventus for a long time, the club has always demonstrated a keen interest in me.
"I admire several Juve players; it will be magnificent to play with them. The presence of other champions at Juventus will inspire me to give everything for the sake of the club.
"The interest between me and Juve was mutual. I come to Juve, one of the best clubs in the world and the best in Italy, with the intention to work very hard and I will try to contribute to future success.
"I feel prepared. I know it will be tough, but I am ready to play in Serie A, one of the best leagues in the world."
Real Madrid announced that the transfer includes a buy-back option, but Juventus director general Giuseppe Marotta was delighted with the capture regardless.
He added: "Alvaro is definitely one of the best young talents in European and world football.
"He has a winning mentality. There was competition from other clubs, but he wanted the Juve shirt."
