Browne died early Wednesday at Cedars-Sinai Medical Center after a long battle with cancer, said Alan Nierob, a spokesman for the family.
Browne's career included classic theater to TV cartoons. He also was a poet and a former world-class athlete.
His deep, cultured voice was heard narrating the 1995 hit movie "Babe." On screen, his character often was smart, cynical and well-educated, whether a congressman, a judge or a butler.
Born to a Baptist minister in Woodbury, N.J., Browne graduated from historically black Lincoln University in Pennsylvania, where he later returned to teach comparative literature and French. He also was a track star, winning the 880-yard run in the 1952 Millrose Games.
Browne was selling wine for an import company when he decided to become a full-time actor in 1956 and had roles that year in the inaugural season of the New York Shakespeare Festival in a production of "Julius Caesar."
In 1961, he starred in an English-language version of Jean Genet's play "The Blacks."
Two years later, he was The Narrator in a Broadway production of "The Ballad of the Sad Cafe," a play by Edward Albee from a novella by Carson McCullers. In a front page article on the advances made by blacks in the theater, the New York Times noted that Browne's understudy was white.
He won an Obie Award in 1965 for his role as a rebellious slave in the off-Broadway "Benito Cereno."
In movies, he was a spy in the 1969 Alfred Hitchcock feature "Topaz" and a camp cook in 1972's "The Cowboys," which starred John Wayne.
"Some critics complained that I spoke too well to be believable" in the cook's role, Browne told The Washington Post in 1972. "When a critic makes that remark, I think, if I had said, 'Yassuh, boss' to John Wayne, then the critic would have taken a shine to me."
On television, he had several memorable guest roles. He was a snobbish black lawyer trapped in an elevator with bigot Archie Bunker in an episode of the 1970s TV comedy "All in the Family" and the butler Saunders in the comedy "Soap." He won an Emmy in 1986 for a guest role as Professor Foster on "The Cosby Show."
In 1992, Browne returned to Broadway in "Two Trains Running," one of August Wilson's acclaimed series of plays on the black experience. It won the Tony for best play and brought Browne a Tony nomination for best featured (supporting) actor.
The New York Times said he portrayed "the wry perspective of one who believes that human folly knows few bounds and certainly no racial bounds. The performance is wise and slyly life-affirming."
Browne also wrote poetry and included some of it along with works by masters such as Lawrence Ferlinghetti and William Butler Yeats in "Behind the Broken Words," a poetry anthology stage piece that he and Anthony Zerbe performed annually for three decades.