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.
Lukaku, whose father Roger also played professional football in Belgium, joined Anderlecht aged 13 and became a household name when he was top scorer in the domestic league with 15 goals in the 2009/10 season at just 16 years old.
He was voted runner-up for Belgian player of the year in 2010 behind his Anderlecht strike partner Mbark Boussoufa after the pair had helped the club win their 30th league title.
The powerful left-footed Lukaku netted 16 league goals last season and has scored twice in two games this term.
Anderlecht did not disclose how much Chelsea had agreed to pay for the six-foot four-inch Lukaku but British media last month reported that they had an 18 million pounds bid turned down by the Belgian club.
Lukaku, who has played 10 games for Belgium, scored his first two international goals against Russia in November.
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