The Spaniard was reported to be close to a move to the Bianconeri on Friday and it appears that the transfer is to go ahead.
"I am very happy to be here," he told Sky Sport Italia. "I will have my medical tomorrow and can't wait to start my new adventure.
"The medical is tomorrow. I hope everything goes well."
According to Football Italia, Morata will cost Juventus €18m (£14.25m), but Real Madrid are believed to have inserted a buy-back option into his contract worth €35m (£27.7m).