The Sydney native had begun a career in insurance when he started to appear in local amateur productions and got hit with the acting bug. Moving to London, he honed his craft on stage and then returned Down Under. Brown made his feature debut in a bit role in "The Love Letters From Teralba Road" (1977) and went on to appear in eight more films over a two year period, notably as the editor in Philip Noyce's "Newsfront" (1978) and as a thief who bungles a robbery in "Palm Beach" (1979). Despite the international attention he won for "Breaker Morant", Brown continued to appear in Australian films until the mid-80s. His rugged good looks generally caused him to be cast as small-time crooks. Director John Duigan offered Brown two of his best roles of this period: a bookstore owner drawn to a prostitute (Judy Davis) in "The Winter of Our Discontent" (1981) and a nightclub owner who rekindles a long ago affair in "Far East" (1982).

Brown first came to the attention of American TV viewers in the miniseries "A Town Like Alice" when it aired on PBS' "Masterpiece Theater" in 1981. He gained mainstream success and an Emmy nomination as Luke O'Neill, the ne'er-do-well husband of the heroine (Rachel Ward) in the popular ABC miniseries "The Thorn Birds" (1983). While he lost the girl on screen to rival Richard Chamberlain, Brown fared better in real life; he and Ward were married in 1983. His first US-made feature was "F/X" (1986), an implausible, but entertaining thriller in which he was a movie special effects genius who becomes embroiled in an assassination plot. (For the inevitable sequel, "FX2 - The Deadly Art of Illusion" (1991), Brown added executive producer to his credit.) He and Ward co-starred as husband and wife in the underrated "The Good Wife" (also 1986), which focused on an unhappily married woman in 1920s Australia. Brown is perhaps best-remembered as the bartender-mentor to Tom Cruise in the fluffy "Cocktail" and as Sigourney Weaver's married lover in the biopic of Dian Fossey "Gorillas in the Mist" (both 1988).

Although his feature output has slowed somewhat in the 90s, Brown has continued to work in TV-movies (e.g., "Dead in the Water", USA Network 1991; "Jules Verne's 20,000 Leagues Under the Sea", ABC 1997). Perhaps his best work of the decade was his superb award-winning turn as a local tough guy who believes he has been double-crossed by a young street hustler in the Australian-made "Two Hands" (1999). Brown also reteamed with his wife Rachel Ward to play estranged lovers in the Showtime miniseries "On the Beach" (2000). After a few low-profile projects both good--such as the Australian gangster drama "Dirty Deeds" (2002)--and not-so-good--like the Peter Weller actioner "Styx" (2001), the actor gave a winning supporting turn as a thrill-seeking, extreme sports-minded CEO hoping to get insured in his latest position in the lightweight Ben Stiller-Jennifer Aniston pairing "Along Came Polly" (2004).