The sale of the 18-year-old striker has been announced on the Belgian club's official website, although the fee is unknown.
Lukaku will finalise a move to Stamford Bridge once a medical has been passed and personal terms agreed.
"He's an interesting young prospect. The situation is now that we have to position ourselves to maybe get this kind of talent," said Chelsea manager Andre Villas-Boas.
The Belgian has scored 33 goals in 73 games for Anderlecht.