Born in Leporano, in the province of Taranto, Greco moved in Turin as a child.
[1][2] In 1964 he graduated at the Centro Sperimentale di Cinematografia, then, two years later, he started an activity as documentarist for RAI TV.
[1] In 1971 he attended Roberto Rossellini accompanying him in Chile for a filmed interview with Salvador Allende.
[1] In 1974 Greco made his directorial debut in a feature film with Morel's Invention that, well-received from critics, marked him as a real promise in Italian art cinema.
[3] In 2004 Greco, together with Francesco Maselli, founded and organized the "Giornate degli Autori" section at the Venice Film Festival.