The 19-year-old is expected to take part in Kilmarnock’s friendly against Valladolid on Thursday.
“Ben has potential and we are delighted to have him on board,” Kilmarnock boss Mixu Paatelainen told the Daily Record.
“He is young but has good ability and will go into straight into the fight for a first-team place.
“Everything has been agreed with Chelsea and I expect he will play some part against Valladolid.”
