Noyce was born in Griffith, New South Wales, and began making short film at the age of 18, starting with Better to Reign in Hell, using his friends as the cast. He joined the Australian Film & Television School in 1973, and released his first professional film in 1977.

After his debut feature, Backroads (1977), Noyce achieved commercial and critical success with Newsfront (1978), which won Australian awards for Best Film, Director, and Screenplay.

Noyce worked on two miniseries for Australian television with fellow Australian filmmaker George Miller: The Dismissal (1983) and The Cowra Breakout (1984).

Miller also produced the film that brought Noyce his greatest acclaim in the United States — the thriller Dead Calm (1989) which turned Nicole Kidman into a star. His greatest commercial success to date has been the Tom Clancy spy thriller Clear and Present Danger (1994) starring Harrison Ford.

Noyce achieved great acclaim in Australia for the "stolen generation" picture, Rabbit Proof Fence, which won the Australian Film Institute Award for Best Film in 2002.

He was married to film producer Jan Chapman from 1971-1977, and is presently married to producer Jan Sharp. They have one child.