The Ligue 1 champions have said Mbappé's contract was "legally amended" and that he reneged on commitments when he left the club to join Spanish giants Real Madrid during the summer transfer window.
PSG said last month that Mbappé, 25, had refused an offer from the LFP to mediate on the issue.
The LFP's National Joint Appeals Commission heard the parties on Oct. 15 and announced on Friday it had ruled in favour of Mbappé.