He was brought to Chelsea from Fiorentina in a £23 million deal under Jose Mourinho in the 2015 January transfer window, but failed to make an impact on the pitch, while he also struggled to settle in London.
Cuadrado spent last season on loan at Juventus before returning to Chelsea, with Antonio Conte keen to keep him at the club having initially tried to sign him when he was coach of the Serie A champions.
Current Juve boss Massimiliano Allegri had to be patient, though, in his attempts to re-sign Cuadrado, with the complexity of the deal and Conte's wishes delaying it until the final moments on transfer deadline day last summer.
Paulo Dybala goals for Juventus
Paulo Dybala's magnificent double against FC BarcelonaPosted by Goal.com on Wednesday, 12 April 2017
Chelsea have no option to recall Cuadrado and his loan extends for the entire duration of his contract with the Stamford Bridge club. The deal will see Chelsea earn a minimum of £13 million through loan fees over the course of the three years but are likely to earn much more through bonus-activated fees related to Juventus' success on the pitch.
There is an extra £3.5 million that can be earned by Chelsea from Juventus performing well in Europe and their domestic competitions, but there is also a £10 million obligation to buy him, if Juventus win the Serie A title. His wages are also covered by Juventus, making him one of the best-paid players in Italy.
Chelsea may end up earning a £500,000 profit on Cuadrado's, so-called, loan move if all clauses are activated. This is on top of the £4 million fee they received last year for loaning him to Turin.
Cuadrado proved his quality at the Juventus Stadium against Barcelona but Conte can celebrate a good deal, despite losing a player who he has always rated.