Lukaku, 18, will join the Premier League side subject to passing a medical and agreeing personal terms.
"It's a shame we have to let go of Romelu, who was scouted and trained by Anderlecht, but the transfer is a win-win situation for the player and the club," Anderlecht manager Herman van Holsbeeck told the club website.
Chelsea's new coach Andre Villas-Boas said last month he had inherited one of the oldest squads in the Premier League and the club, who were runners-up to Manchester United last season, planned to invest more in younger players.
"The situation with Lukaku is that he's a very interesting young prospect and we have to be able to position ourselves to get this kind of talent," Villas-Boas was quoted as saying on the Chelsea website on Saturday.
"And not only him but other talent that we are scouting at the moment," he added after Chelsea beat Rangers 3-1 in a friendly at Ibrox ahead of the Premier League season which kicks off next weekend.
