A cause of death was not revealed, but Cox had been struggling with health issues in recent years. He had long battled cancer, and underwent a liver transplant in 2009.
Cox, who was born in the Netherlands and relocated to Australia in 1965, first broke out with "Lonely Hearts" in 1981. The romantic comedy starred Wendy Hughes and Norman Kaye, and would go on to win the AFI Award for best film.
After his initial breakthrough, the director released "Man of Flowers" in 1983 and "My First Wife" in 1984 to international acclaim. He continued to work even in recent years, despite battling illnesses.
See photos of Paul Cox from throughout his career:
Last year, Cox wrote and directed the semi-autobiographical "Force of Destiny." The film starred David Wenham as a man awaiting a liver transplant.
His credits include 12 documentaries, with the most recent being 2012's "The Dinner Party." He also directed "Nijinsky: The Diaries of Vaslav Nijinsky" in 2001, with Derek Jacobi as the voice of the Russian ballet star.
Cox's daughter, Kyra, tweeted a tribute to him on Saturday. "Goodbye my beautiful daddy," she wrote.