Goal understands the Brazilian is set to seal a sensational £40 million move to the French champions after the two clubs agreed 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 centre-back pairing.
"The move is now subject to David Luiz agreeing personal terms with PSG and passing a medical examination."
Luiz joined Chelsea from Benfica in January 2011 for a fee of £21.3 million 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.
Chelsea, meanwhile, are set to spend heavily this summer with Atletico Madrid striker Diego Costa their top target, with the Blues having already agreed a £35m deal for the Spaniard.
Laurent Blanc's men had been expected to curb their spending after being sanctioned by Uefa for breaching Financial Fair Play regulations.
PSG were fined €60m by the governing body and had their Champions League squad reduced to 21 players for next season.