The 27-year-old, who is preparing to represent Brazil at the World Cup, looks set to seal a switch to the Ligue 1 champions after a deal was announced on Friday.
|11/1||Brazil are 11/1 with bet365 to beat Croatia 4-0 on June 12|
"Thanks Chelsea for the three-and-a-half years of great partnership," he wrote on his Facebook page.
"I've made good friends, won many titles and those memories will last with me forever.
"I'd like to thank my team-mates, all staff and all supporters (my geezers).
"I'm leaving with great sadness but at the same time excited for the new challenge that lies ahead in this great club in a city that have always enchanted me.
"It's a new stage, new challenge and together we will go even further."
PSG are set to pay €49.5 million for Luiz, a world-record fee for a defender.