Chelsea have snapped up the Belgium youth international playmaker, 15, who has yet to sign a professional contract.
Anderlecht chairman Roger Vanden Stock fumed: "I'm very disappointed. We agreed with Charly's father he would stay with us a few more years.
"Chelsea know Belgian clubs can't give players contracts until they are 16. We're going to try to get some serious compensation from them."
Musonda's two brothers, Lamisha, 20, and 18-year-old Tika will also swap the Belgian champions for Stamford Bridge. Dad Charly Sr is an ex-Zambia international.