Hector was born in England however chose to represent Jamaica at international level, being selected in their squad for the 2015 Copa América.
Hector, a former Millwall trainee, has had 11 loan spells since joining Reading in 2009. These stints include time with non-League clubs Bracknell Town, Havant & Waterlooville and Horsham.
Earlier this summer, he signed a new three-year deal with the Royals after impressing in his first full season in their side.
He has made 63 appearances in all competitions including five this season.
Hector’s arrival will be Chelsea’s second defensive reinforcement on transfer deadline day following the arrival of Papy Djilobodji on a four-year deal. The Premier League champions made their move for the 26-year-old after seeing their overtures for Everton’s John Stones repeatedly rebuffed.