De Sciglio, an expected replacement for the departed Dani Alves, was reported to be in China earlier this week meeting his new Juve teammates.
He has now returned to Italy to complete the final details of the proposed €12m transfer, with formal confirmation likely to follow by the end of the week.
The 24-year-old Italy international has been with the Rossoneri since the age of 10 but now takes the next step in a career that has so far only seen him win a Supercoppa Italiana.
While naturally right-footed, he is also at home on the left and so offers plenty of versatility.
An announcement over Wojciech Szczesny's arrival from Arsenal is also expected sooner rather than later after he was in Turin for his own medical earlier this week.
Juve have already completed deals for Douglas Costa and Rodrigo Bentancur this summer, with the permanent transfers of Medhi Benatia and Juan Cuadrado also finalised.