The Colombian has arrived from ACF Fiorentina of Serie A.
The player, who shone in Serie A last season and at the World Cup in the summer, has reportedly joined for a fee on a four-and-a-half-year contract for a fee reported by the BBC to be in the region of £23.3 million, rising to £26.8 million dependent on appearances.
The deal came about after Andre Schurrle agreed his move to VfL Wolfsburg just before the German deadline expired earlier today.
For Chelsea it is an excellent coup considering the style of player he is. He is an attacking midfielder not afraid to track back, a facet Jose Mourinho demands from his midfield players in order for his strategies to work.
Cuadrado is clearly very pleased with the move to Chelsea. The 26-year-old has taken to his official Instagram account this evening to state that his move to Stamford Bridge is a 'dream come true'.
Chelsea fans will be hoping he can help the club to a Premier League title and perhaps a League Cup and/or Champions League medal this campaign.