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.
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."
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."
