Goal understands the Brazilian is set to seal a sensational 40 million pound move to the French champions after the two clubs agreed to a deal.
Luiz has made just 15 starts for the Blues this season after falling down the pecking order with John Terry and Gary Cahill, manager Jose Mourinho's preferred center back pairing.
MORE: Top 25 infamous moments in World Cup history
Luiz joined Chelsea from Benfica in January 2011 for a fee of 21.3 million pounds and has gone on to win the Champions League, Europa League and FA Cup during his time at Stamford Bridge.
However, Luiz has failed to become a regular under Mourinho and becomes another high-profile departure from west London, following Juan Mata who left for Manchester United in January for 37.1m pounds.
Chelsea, meanwhile, are set to spend heavily this summer with Atletico Madrid striker Diego Costa their top target, with the Blues having already agreed on a 35m pound deal for the Spaniard.