"David Luiz is one of the great defensive prospects in world football, and already a Brazilian international," said the Blues chief executive Ron Gourlay. "I am sure he will prove a valuable addition to the Chelsea squad."
Benfica had said previously that negotiations had broken down with Chelsea, with problems emerging over their displeasure with the payment being made in instalments or a cash-plus-player deal being offered.
But Chelsea's latest offer was been accepted and now Luiz is set to link up with fellow Brazilians, defender Alex and midfielder Ramires, at Stamford Bridge.
Luiz arrived in Lisbon from Brazil in 2007 and was a key member of the Benfica side that last season clinched the Portuguese title for the first time in five years, missing only one of 30 league matches.
But having represented Benfica in the knockout stage of the Champions League, Luiz will not be eligible to represent Chelsea in this season's competition.
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