Ferracci, initially expected to leave at the end of the season, confirmed his departure during an event on Monday.
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Arnault, representing the club's majority-owning family, will assume the presidency, subject to approval by the Administrative Council on November 9.
Ferracci will become honorary president, with the November 1 clash against Monaco at Stade Jean Bouin expected to mark his farewell.
The outgoing president will also transfer his 28.9% stake to Agache Sport, LVMH's sporting subsidiary, while Red Bull retains its 10.6% holding.
"It is the right time for me to pass the torch," Ferracci said, according to L'Équipe.
He departs with Paris FC sitting third in Ligue 1, level on points with leaders Lyon.