The 28-year-old forward has made 83 appearances for Juve, who have activated a clause to buy the Colombian after he failed to secure a regular starting spot at Chelsea following his 23.3 million pounds ($30.28 million) move from Fiorentina.
"The permanent transfer fee of 20 million euros is to be paid in three annual instalments starting from the 2017/2018 financial year," Juve said on their website.
Under Massimiliano Allegri's guidance, Cuadrado has won two Serie A titles and two Coppa Italia trophies and helped Juve reach next month's Champions League final against Real Madrid.
(Editing by Alison Williams)
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