The midfielder came through PSG's academy and made his debut for the club in February 2013.
In doing so, at the age of 16 years, eight months and four days, Coman became the youngest player to represent PSG, taking the record from Nicolas Anelka.
Now 18, Coman has already played for France at Under-21 level and will have the opportunity to continue his career in Serie A.
A statement on Juve's official website confirmed the signing and described Coman as a "technical and imaginative player... with athletic power out of the ordinary".
Coman made a further two Ligue 1 appearances for PSG following his maiden outing, featuring as a substitute against Bordeaux and Montpellier last term.
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