After weeks of speculation, Chelsea announced Cuadrado's arrival on Monday, shortly after Andre Schurrle's departure to Wolfsburg.
Cuadrado spent five-and-a-half years in Italy, initially with Udinese before a move to Fiorentina in 2012 following a loan spell at Lecce.
"I am very happy and thankful for this opportunity I’ve been given," he told Chelsea's official website.
"This is a great club and honestly it is like a dream to join the Chelsea family and to know that the manager believes in me. I’m happy."
Cuadrado has five goals in 37 appearances for Colombia, and he was a key member of the side that starred at last year's World Cup in Brazil, before their quarter-final exit at the hands of the hosts.
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