A further €500,000 in add-ons have also been included in the deal, with De Sciglio putting pen to paper on a long-term contract that will keep him in Turin for the next five years until 2022.
Having arrived for a medical earlier this week, 24-year-old De Sciglio is the second Juve signing in the space of two days after goalkeeper Wojciech Szczesny was unveiled on Wednesday.
Douglas Costa and Rodrigo Bentancur have also joined the club this summer, while the loans of Juan Cuadrado and Medhi Benatia have been made permanent as well.
Milan native De Sciglio is expected to replace Dani Alves in the Juve line-up after the veteran Brazilian cancelled his contract and moved to Paris Saint-Germain as a free agent.
He and the rest of the squad now fly to the United States for pre-season tour.
De Sciglio has been capped over 30 times by Italy since an international debut in 2013 and had been a regular with Milan since 2012 after first breaking through as a teenager.