The 26-year-old has been with the Florence-based outfit since 2012, having initially joined them on a loan deal from Udinese.
The Viola are now said to have bought the full rights of the winger from Udinese, with the player himself confirming the deal.
“I am very happy that Fiorentina bought me, they are a great club and Florence is a beautiful city,” he told Nuevoestadio.com.
“Now I don’t think about my club future, I hope to finish the World Cup very well with Colombia, I only think about that.”
Cuadrado’s performance for Fiorentina in the 2013/14 season during which he helped them finish fourth in Serie A have attracted attention from many of Europe’s bigger clubs.
Barcelona are reportedly interested in the former Independiente Medellín winger, but Prade has dismissed those rumours.
“There is nothing,” A Bola quotes him as saying. “There is no offer from Barcelona or anyone else (for Cuadrado).”
Meanwhile, Fiorentina have been linked with a move for Stuttgart striker Vedad Ibisevic.
The Bosnia and Herzegovina international scored only 10 goals and provided two assists in 27 Bundesliga appearances for Huub Stevens’ side last season.
However, Stuttgart president Bernd Wahler insists that Ibisevic is an important part of the team.
“Actually, Vedad Ibisevic still is a player of our clubs, he is a good striker,” he said. “No one should really forget those periods in which Vedad was the main guarantee of goals in our attacking line.”