The Italian side confirmed Cuadrado has travelled to Italy and posted a number of pictures showing the smiling winger being welcomed by excited fans.
The Columbian is set to undergo a medical with the Italian champions today, before completing his loan switch with the option to buy.
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The 27-year-old forged his reputation as a pacey and skilful wide player during a three-year spell at Fiorentina, where he scored 26 goals in 106 games, and will be hoping to rediscover his form in the black and white of the Champions League finalists.
His career at Chelsea was short lived, failing to make an impact in the 15 games he played for the Blues following a £23.3 million deal.
Pedro's arrival at Stamford Bridge signalled the end of Cuadrado's time in London after just seven months, but neither party will be too bothered about going their seperate ways.
Chelsea have gained a player with a proven ability and track record at the highest level, while Cuadrado gets the opportunity to play Champions League football in a country that propelled him onto world footballs centre stage.
It is a shame the Columbian could not rediscover the form he produced at the World Cup and in Florence during his time at West London, but he was very rarely given an opportunity to shine, playing second fiddle behind Willian as Chelsea won the title.
However when given the nob by Mourinho he failed to impress and often looked uncomfortable with the high pressing, tough tackling nature of the Premier League.
A move to Serie 'A' will allow him to rediscover his form, much like it did Mohamed Salah, but for both of them, their careers in English football are over, for now.