The 21-year-old has long been expected to complete a move to the Italian champion after seeing first-team football hard to come by under Carlo Ancelotti in the Spanish capital last season.
Morata has now arrived in Italy to complete a medical on Wednesday and the Spain Under-21 striker says he is looking forward to life with the Bianconeri.
"I am very happy to be here," he told Sky Sport Italia on his arrival. "I will have my medical tomorrow and can't wait to start my new adventure."
Juventus also took the time to welcome Morata to the club, posting a picture of the player wearing a Juve scarf through its official Twitter account.
Morata's transfer is expected to cost 18 million euros, with Madrid including a buyback option in the player's contract.