Juventus confirmed the news in a statement released on their website on Monday evening, and revealed they will pay Chelsea £17.3m in three instalments for the Colombia global who has spent this season on loan in Turin.
However, the reinvention of Victor Moses as a right wing-back essentially spelt the end of Cuadrado's hopes and he was allowed to return to Juve on what was a three-year loan deal.
Cuadrado moved to Chelsea in February 2015 after impressing with Fiorentina.
With three years also remaining on Cuadrado's Chelsea contract, the loan basically amounted to a lease with 0% interest, with Juventus set to pay €5m annually (plus annual add-ons of up to €4m based on performance targets).
In a club statement, Juve said: "Two seasons at Juventus, two league titles, as many Italian Cup, a Champions League final on the horizon, and now certain to stay at Juventus".
"The permanent transfer fee of 20 million euros is to be paid in three annual instalments starting from the 2017/2018 financial year".
Cuadrado has signed a long-term contract with the club, keeping him in Turin until June 2020.
Cuadrado couldn't settle in West London however, playing just 15 times and failing to find the back of the net once.