"The move is now subject to David Luiz agreeing personal terms with PSG and passing a medical examination," Premier League club Chelsea said on their website (www.chelseafc.com).
British media reported that the versatile 27-year-old would command a world record fee for a defender of between 40 million ($67.37 million) and 50 million pounds ($84.21 million).
That would surpass the 36 million pounds Qatari-backed PSG paid for Luiz's Brazil team mate Thiago Silva in 2012 although neither club disclosed the financial terms of their agreement.
The easily recognisible Luiz, with his long and shaggy hair, joined Chelsea in January, 2011 from Benfica for about 21 million pounds and helped the west London side win the Champions League for the first time the following year.
Strong, energetic and armed with a powerful shot, Luiz likes to venture forward but can be somewhat erratic and prone to the odd defensive lapse.
He has made 143 appearances for Chelsea in 3-1/2 seasons at Stamford Bridge, scoring 12 goals.
PSG said in a statement that they hoped to reach a quick agreement with Luiz, who can also play as a defensive midfielder and is part of Brazil's World Cup squad for the finals which start next month.
"In accordance with the player's wish to prepare for and play in the World Cup in his home country and 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, and on the other, between the Parisian club and the player in order to formalise the transfer as soon as the transfer window opens (on June 10)," the club said.
PSG, who strolled to the Ligue 1 title but lost to Chelsea in the Champions League quarter-finals, were last week fined up to 60 million euros ($82.23 million) and had their squad capped for next season's European campaign after breaching UEFA's Financial Fair Play (FFP) rules.
Wealthy Premier League champions Manchester City were hit with the same punishment and as part of their settlement with European soccer's governing body, both clubs also agreed to curbs on transfer spending over the next two seasons.
($1 = 0.5938 British Pounds)
(Writing by Justin Palmer; editing by Ken Ferris)
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