Conti was an orchestra director by age fifteen. In 1974, he began as a film music director. His big break into celebrity came in 1976, however, when he was hired to choose the music for the movie that also made Sylvester Stallone famous: Rocky. Conti was credited on the cover of the movie's soundtrack album.
Conti also worked for some other films and, eventually, for television series. In 1983, he was the musical director of The Right Stuff, and in 1984, he was hired to collaborate in The Karate Kid. He also worked as musical director of the television shows Dynasty and The Lifestyles of The Rich And Famous.