Margarita Louis-Dreyfus, Marseille's billionaire owner, said in April that she would sell the club following poor results and protests from fans.
McCourt, speaking at a news conference, said: "I'm very excited about making Marseille a champion again."
A deal is set to be completed by the end of the year and no fee has yet been disclosed.
Appearing alongside Louis-Dreyfus and Marseille mayor Jean-Claude Gaudin, 63-year-old McCourt said he wants a team that can compete "year in, year out" to win Ligue 1.
Marseille, who finished 13th in 2015/16 and lost to PSG in the French cup final, are 11th after three games this season.
Frank McCourt, the former owner of the LA Dodgers baseball team, is set to buy French Ligue 1 club Marseille.