The 18-year-old has been linked with the Blues throughout the summer and scored 16 goals in 37 league appearances last season and already has two to his name in two games in the current campaign for the Brussels club.
A statement on Anderlecht's official website www.rsca.be read: "RSC Anderlecht and Chelsea have reached an agreement regarding the transfer of Romelu Lukaku. Subject to the results of medical tests and the conclusion of negotiations between the player and the English club, Romelu Lukaku will therefore move into the colours of the London club."
Anderlecht general manager Herman van Holsbeeck added on the official website: "We regret the departure of Romelu...but the agreement is a win-win situation for the player and RSC Anderlecht. The club's management is committed to finding a good replacement in the short term.
"We wish him every success for the rest of his career."
The player posted a comment on Twitter which read: "I have an announcement to make...Next week I'm going to London for the medical tests."
Chelsea boss Andre Villas-Boas is now closing in on the third signing of his reign, and admitted after Saturday's friendly against Rangers that a deal was close.
He said: "He is a very interesting young prospect and the situation is now that we have to position ourselves to maybe get this kind of talent.
"So I would say that anything can happen."
The Blues reportedly had an ?£18million bid for the player turned down last month.
Source: PA
Source: PA