The 26-year-old Colombia international has signed a four and half year deal and could make his Blues debut against Aston Villa this weekend.
The transfer was completed following Chelsea’s sale of Germany World Cup winner Andre Schurrle to Wolfsburg but there was no mention of Mohamed Salah, who it was suggested might be moving to Florence on loan as part of the deal.
Cuadrado signed for Fiorentina from Lecce in 2013 and impressed in Colombia’s run to the quarter finals at last summer’s World Cup in Brazil, scoring in the 4-1 victory over Japan.
He has since scored six goals in 23 appearances in Italy and the Chelsea website said: “Cuadrado plays predominantly behind a striker, but he is also comfortable on either flank.
“Pacy and agile, he is a purposeful attacking threat with an eye for the spectacular.”
And Cuadrado said: “I am very happy and thankful for this opportunity I’ve been given.
“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.”