The 19-year-old spent time with League One side Tranmere last season and will now continue his education with spell in the SPL.
Paatelainen is pleased with the youngster's ability and expects him to challenge for a first-team place this season.
"Ben has potential and we are delighted to have him on board," 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."