The festival is yet to make an official announcement but Lescure's appointment was confirmed when French Minister of Culture and Communication Aurelie Filippetti tweeted a congratulatory message, according to the Hollywood Reporter.
The Lescure, 68, will replace Jacob, who served as the president of the festival since 2001.
"Congratulations to Pierre Lescure, who has been unanimously elected as president of the Cannes Film Festival, succeeding Gilles Jacob," Filippetti tweeted.
Thierry Fremaux is the director of the Cannes fest.