The French club has reportedly tied Luiz to a four-year deal the 27 year-old having an option for a 5th year as well which would take him to 32 years of age if he stayed the full term.
PSG were fined for their breaching of FFP rules, so the move comes as a bit of a surprise with the likes of Marquinhos and Alex now more likely to leave the club to fund the move.
Chelsea released a statement on Friday: "Chelsea football Club and Paris Saint-Germain have agreed terms to the transfer of David Luiz to the French club. The move is now subject to David Luiz agreeing to personal terms with PSG and passing a medical examination."
PSG also released a statement of their own."To respond to the desire of a player to prepare and play the World Cup in his own country in the best conditions possible, the will of the two clubs and David Luiz was to come to an agreement as quickly as possible between Paris Saint-Germain and Chelsea, on the one hand, and between the Parisian club and the player on the other in order to make the transfer official as soon as the transfer window opens."
The Brazil international made just 19 appearances in the EPL with Gary Cahill and John Terry being preferred at the back which undermines the enormous price tag which PSG were prepared to pay.