"It's a deal that has been done, although from my point out of view, I'm disappointed by it. However, the club has done the right thing," Montella told a news conference.
"He is a professional and always wants to play, I'm happy for him because he is going to a top team," he added.
Montella also hinted that Chelsea forward Mohamed Salah would be joining Fiorentina as part of the deal.
"A top player is leaving but I see similar characteristics in Salah," he said.
Cuadrado, 26, has been the subject of transfer speculation since the World Cup, where he was one of the outstanding players in the Colombia team who reached the quarter-finals.
Cuadrado, worth around 32 million euros (24.02 million pounds)according to the specialist website Transfermarkt.de, has been at Fiorentina for two-and-a-half seasons.
He previously spent two seasons at Udinese and one with Lecce. He began his professional career with Independiente Medellin in his homeland.
(Writing by Brian Homewood in Berne, editing by Ed Osmond)
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