The Brazilian now only needs to agree personal terms and pass a medical to become the most expensive defender in the world, with the fee potentially rising to £50m.
PSG hold the current record for a defender, having paid AC Milan £35m for Thiago Silva. And they also paid the third biggest fee for a defender, having splashed out £27m for Roma's Marquinos last year. Rio Ferdinand's £29.1m move from Leeds to Manchester United is in second place.
A statement on Chelsea's website confirmed: "Chelsea Football Club and Paris Saint Germain have agreed terms for the transfer of David Luiz to the French club.
"The move is now subject to David Luiz agreeing personal terms with PSG and passing a medical examination."
The Paris club have sent their doctors to Brazil where Luiz is training with the national squad ahead of the World Cup.
PSG have confirmed that the deal will go through on 10 June, and that they and the Blues have announced it now so Luiz can concentrate on the World Cup.
A statement on the Ligue 1 winners' official website read: "Paris St Germain, Chelsea FC and David Luiz would like to confirm that they reached an agreement regarding the terms of an upcoming transfer of the Brazilian defender that would occur during the next transfer window which is to start on 10 June 2014.
"In accordance with the player's wish to prepare for and play in the World Cup in his home country in the best possible conditions, both clubs and David Luiz wished to reach an agreement as soon as possible between, on the one hand, Paris St Germain and Chelsea FC, and on the other, between the Parisian club and the player, in order to formalise the transfer as soon as the transfer window opens."
Luiz joined Chelsea from Benfica in 2011, in a £23.5m deal during the January transfer window, and he still had two years left on his contract at Stamford Bridge.
But Blues boss Jose Mourinho now looks set to more than double Chelsea's money, and that cash could go towards a huge bid for Atletico Madrid striker Diego Costa.
The 27-year-old has been deemed surplus to requirements under Mourinho, who recently gave skipper John Terry a one-year extension to his contract and used Gary Cahill at centre-back for most of the season.
Branislav Ivanovic is also capable of playing as a centre-back, and Mourinho - who has used Luiz predominantly as a defensive midfielder - is also known to be a fan of rising youngster Tomas Kalas.
Qatar Sports Investments have ploughed millions into PSG, allowing them to sign the likes of Zlatan Ibrahimovic and Edinson Cavani. They were knocked out of the Champions League by Chelsea in the quarter-finals this season.
The French giants were fined £48.5m by UEFA this month for breaching the Financial Fair Play rules.
But coach Laurent Blanc says that will not stop him improving his squad, and admitted to Le Parisien newspaper he is a big fan of another Chelsea star, Eden Hazard, without revealing whether he would make a bid.
"Hazard is the kind of player who can be decisive," Blanc is quoted as saying.
"You can talk about all kinds of things; tactics, strength of the team, individual class, but a player who is capable of beating three or four players is something else. You never know what to expect from him."
But Blanc confirmed winger Jeremy Menez is definitely leaving and former Chelsea defender Alex could also be on his way out as he tries to make room in his squad for new signings.