The Premier league club's manager Jose Mourinho is happy to stick with English centre-backs John Terry and Gary Cahill and allow Luiz to link up with fellow Brazil international Thiago Silva in the Paris Saint-Germain defence.
The clubs announced on Friday that they had agreed a fee for Luiz which British media estimated was between 40 and 50 million pounds - a world record for a defender, beating the 36 million PSG paid for Silva in 2012 - in a deal that suits all parties.
Chelsea, moving closer towards breaking even, will be able to give their Portuguese coach Mourinho funds towards the new striker he covets and French champions PSG have recruited one of the potential stand-out players at next month's World Cup.
Luiz, 27, is expected to play alongside Silva at the finals in Brazil, although he is equally capable of filling the role of a defensive midfielder.
Indeed, some pundits feel he is better suited to that position. Rafael Benitez played him in front of the back four during his brief spell as Chelsea coach, and Mourinho contradicted an earlier promise by sometimes doing the same.
Playing further forward minimises the danger of conceding a goal from Luiz's occasional rushes of blood to the head, as well as offering more opportunities to utilise his formidable shooting power.
Chelsea supporters still recall one stunning goal from distance against their west London neighbours Fulham in April 2013.
Even when playing in defence Luiz has always loved to burst forward on the ball, often risking being caught out of position.
The shaggy-haired player, full name David Luiz Moreira Marinho, was a midfielder in his younger days in Sao Paulo before being converted to defence as a teenager with Vitoria.
He was still only 19 when following the well-trodden path from Brazil to Portugal in 2007, joining Benfica on loan and then permanently.
Portuguese League Player of the Year in 2009-10, he was rewarded with a step up from Brazil's Under-20 side to the senior squad under Mano Menezes.
In January 2011 he joined Chelsea for a reported fee of £21.3 million plus midfielder Nemanja Matic.
Among his final matches for the London side were the two Champions League quarter-final ties against PSG last month.
Chelsea won the second leg 2-0 to go through on away goals, after which Mourinho singled out Luiz's performance - in midfield - describing him as "a monster".
An expensive monster perhaps, but one the Ligue 1 club will be delighted to have on their side.
- Sports & Recreation
- Jose Mourinho
- Thiago Silva
- Paris Saint-Germain