The Brazil international refused to depart the pitch during the club's 2-1 win over Marseille despite seemingly sustaining an injury, but the pair have now resolved the issue
The PSG coach was ready to replace the defender with Marquinhos in the closing stages of the game after Luiz had seemingly sustained an injury, but the former Chelsea star refused to depart the field of play.
Blanc, who eventually substituted Blaise Matuidi instead, was not happy with Luiz's actions, but the duo have now held talks to clear the air.
"I spoke with him on Monday morning. We had a very good discussion. Not only a good one, but a very long one as well," Blanc.
"It was important to have a chat. We needed to clarify what happened and to speak clearly and sincerely. Our conversation went on for quite a long time.
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"It was impossible not to talk about what happened and I am quite pleased with the outcome of our conversation.
"I obviously won't disclose what we discussed, but we needed to have this talk in order to keep having a good relation with him."
PSG take on Lyon in the Coupe de France on Wednesday, but they will have to make do without the services of Marco Verratti due to injury, much to the frustration of Blanc.
"Verratti is very important. He takes his responsibilities and sometimes even too much," he added. "I prefer that over the opposite to be fair. He loves taking risks. He likes having the ball and never hides.
"I once said that nobody is irreplaceable, but we really miss Marco when he is not there. He is very important to the way we play and for our philosophy.
"But we will have to make do without him. We have put in some great performances without him as well."