Goal understands the Italy international - who has also been linked with Inter and Chelsea - has agreed a five-year deal with the Serie A champions worth €4m-a-year having made it clear that he wants to leave La Viola.
His current deal in Florence runs until 2019, and Fiorentina are hopeful of securing a deal worth an initial €40m plus another €10m in add-ons for the 23-year-old.
Juve have also hinted that he would be offered the chance to wear the legendary No.10 shirt in Turin, which has previously adorned the likes of Michel Platini, Alessandro Del Piero and, most recently, Paul Pogba.
Having broken into the Fiorentina side during the 2014-15 season, Bernardeschi has gone onto make 93 appearances for the club, scoring 23 goals.
Such form saw him receive a first international call-up in March 2016 and he has since made nine appearances for the Azzurri, scoring his first goal during last month's victory over Liechtenstein.
Juve boss Massimiliano Allegri has been on the lookout for a natural wide player throughout the summer and Bernardeschi sits top of his list, with Bayern Munich's Douglas Costa as a potential alternative.
Should a deal be secured, it may not be the only business the two clubs do this summer, with Fiorentina keen on both Tomas Rincon and Stefano Sturaro.