Morata joins Juve on loan from Atletico for €10m with an option to buy for €45m, but the loan can be extended for another €10m.
The striker passed his medical at the Continassa centre in Turin on Tuesday morning.
Juve confirmed it is a loan for the 2020-21 season at a cost of €10m with option to buy for €45m, payable in three instalments.
Juventus have the option to extend the loan until the end of the 2021-22 season for a further €10m.
If they do that, then the option to buy will be at a cost of €35m from 2022, again payable in three instalments.
Morata will wear the Number 9 jersey.