The Colombian wing-back will sign on a four year deal, for a reported transfer fee of £27m.
Cuadrado becomes the first signing for Chelsea in the January transfer window. Fiorentina are also expecting to complete the transfer of Mohamed Salah on loan today.
Upon signing, he 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.’