Chiesa, 22, is considered one of the hottest prospects in Italian football and the move was finalised once Douglas Costa completed a loan move to Bayern Munich.
Juve will pay a total of €10m over the two seasons of the loan with €3m for the 2020-21 campaign and €7m for the following term.
The Bianconeri will pay a fee of €40m to make the deal permanent payable over three years, which could rise by a further €10m.
The winger, whose father Enrico was also an Italy international who played for Fiorentina, made his debut for La Viola in 2016.
He is a regular in the Italy side under Roberto Mancini and has earned 19 caps since his first appearance in 2018.
Chiesa will find his former Viola teammate Federico Bernardeschi at Juve, who left Fiorentina for the Turin giants in 2017.