Luiz will move for £50m, a world record fee for a defender. A statement on Chelsea's official website read: "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 French champions suggested the formalities of the deal will be completed on 10 June to ensure Luiz can concentrate on this summer's FIFA World Cup™ in his native Brazil.
A statement on the French Ligue 1 winners' official website read: "Paris Saint-Germain, Chelsea 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 Saint-Germain and Chelsea, and on the other, between the Parisian club and the player, in order to formalise the transfer as soon as the transfer window opens."