After completing his medical on Monday, the Italy international joins on an initial two-year loan deal at a total cost of €10million.
Juve also has a purchase option, which is for €40m and could rise to €50m.
His arrival comes after Douglas Costa departed the club earlier in the day, the Brazilian returning to Bayern Munich on loan for the 2020-2021 season.
Juve had already added midfield duo Arthur and Weston McKennie to bolster the squad, along with forward Alvaro Morata.
Chiesa scored 10 goals in 34 Serie A appearances last term, while he has found the net once in three outings at the start of the new campaign.
The 22-year-old has played 20 times for Italy so far in his career, his solitary goal for the national team coming in a 9-1 win over Armenia in November 2019.