Audi is the son of the Lebanese banker Raymond Audi and Andrée Michel Fattal, the eldest of three children. Audi's family were originally from Saida, but he attended the French Lycée in Beirut. While still at school, he initiated a cinema club and invited speakers including the film directors Pier Paolo Pasolini and Jacques Tati.
From 2005 to 2014, Audi also was the artistic director of the Holland Festival. As of October 2015 he is the artistic director of Park Avenue Armory, while continuing his work as artistic director of the Dutch National Opera.