Rosenberg, who also directed "The Amityville Horror," died of a heart attack Thursday at his home in Beverly Hills, according to his son, Benjamin.
Rosenberg's first film was "Cool Hand Luke," the 1967 drama starring Newman as an inmate on a chain gang who becomes an unlikely hero.
"He was as good as anybody I ever worked with," Newman said in a statement.
"Cool Hand Luke" was nominated for four Academy Awards, with George Kennedy taking home a statuette for best supporting actor. The film also spawned the famous line delivered by Strother Martin as a guard captain: "What we've got here is a failure to communicate."
Rosenberg was nominated for a Directors' Guild Award for the film, but lost to Mike Nichols, who made "The Graduate" the same year.
After "Cool Hand Luke," Rosenberg directed Jack Lemmon and Catherine Deneuve in "The April Fools." He worked with Newman again on "WUSA," "Pocket Money," and "The Drowning Pool."
Rosenberg also directed Robert Redford in the 1980 prison film "Brubaker" and Mickey Rourke in 1984's "The Pope of Greenwich Village." "Amityville Horror" in 1979 was probably his most financially successful film; it has inspired seven sequels to date.
His last film was "My Heroes Have Always Been Cowboys" in 1991.
Rosenberg had started out by directing episodes of television series in the 1950s, starting with "Decoy," which starred Beverly Garland as a New York City policewoman.
He collected more than 300 TV directing credits for such dramatic series' as "The Untouchables," "Alfred Hitchcock Presents" and "The Twilight Zone," and won an Emmy Award in 1963 for an episode of "The Defenders."
Rosenberg is survived by his wife, Margot, and son Benjamin, an assistant editor who worked with his father on many of his later films.