The Blues had long been in negotiations for Cuadrado and the Serie A club's coach, Vincenzo Montella, revealed on Friday that a deal had been put in place, while Mohamed Salah is expected to head in the other direction.
The Colombia international had been at Anfield for the League Cup semi-final first leg clash between Liverpool and Chelsea at the end of January as speculation intensified that he would join Jose Mourinho's ranks.
Having starred for his country at the World Cup, Cuadrado had been linked with summer moves to Barcelona and Manchester United, but no deal ever came to fruition with either club.
Fiorentina insisted throughout January that their prized asset would only be allowed to leave for his release clause of around £26 million.
And it has not been confirmed that he will join the Blues and help the club's push for success in the Premier League, League Cup and Champions League.
Cuadrado moved to Europe in 2009, joining Udinese from Independiente Medellin, before signing for Fiorentina in 2012.
