Willoughby died Friday of cancer at his home in Vence, France, said Claire Willoughby, a daughter-in-law.
The rise of Life and Look magazines created a demand for more than routine photo stills from movie sets and led to a career for Willoughby that spanned three decades.
It took off in 1954 when Warner Bros. asked him to photograph Judy Garland's final scene on the set of "A Star Is Born." His portrait of the freckle-faced star became his first Life cover.
Over the next 20 years, he made now-classic photos on the sets of about 100 films, including the 1960s movies "The Graduate," "My Fair Lady," "Rosemary's Baby" and "Who's Afraid of Virginia Woolf?"
Writing in 1974 in The Times, entertainment critic Charles Champlin called Willoughby one of the finest movie-set photographers and said his work was impressive "as photojournalism becomes salon art."
Director Sydney Pollack, who died last year, paid homage to Willoughby in the photographer's 2003 book, "The Star Makers": "Sometimes a filmmaker gets a look at a single photograph taken on his own set and sees the 'soul' of his film right there. It's rare, but it happens, and did so to me in 1969, the first time I looked at work Bob had done during the filming of 'They Shoot Horses, Don't They?' "
He made himself seem invisible, Willoughby later said, by blending in with the movie crew, once he realized they were invisible to the actors.
In turn, he revealed "actors and actresses as themselves, not merely as characters they played," the Times of London reported in 2003.
Willoughby turned his lens on many of the era's movie legends, including Marilyn Monroe, John Wayne, Humphrey Bogart and Elizabeth Taylor. William Holden, Jack Lemmon and Hepburn were "special people" whom he saw socially, the photographer once said.
He became the go-to photographer for Frank Sinatra and the Rat Pack, the raucous group of Las Vegas nightclub entertainers. One of Willoughby's most famous Rat Pack pictures features most of the group in front of the Sands Hotel sign when they were making the 1960 film "Ocean's Eleven."
On an earlier Sinatra film set, "The Man With the Golden Arm" (1955), director Otto Preminger tried to tell Willoughby how to take his photographs. Sinatra was stunned when the relatively young photographer dared to tell Preminger: "You look after your job and I'll look after mine," Willoughby recounted in 2002 in London's Sunday Express.
Willoughby's shots of Sinatra singing at a recording session for the film are now regarded as classics.
The photographer was closest to Hepburn, whom he met in 1953 at Paramount Studios when she was on the cusp of stardom for "Roman Holiday" and he was an established magazine photographer.
While setting up his equipment, he found his eyes constantly "drifting back to that face," he later wrote, which had a "smile that God designed to melt mortal men's hearts."
Magazines snapped up his photographs of Hepburn on movie sets. After shooting her a number of times, he became close enough to follow Hepburn home.
The resulting images were the subject of a 2008 Life book, "Remembering Audrey," which features candid portraits.
According to a Los Angeles Times review of the book, the most striking images were taken off the clock, such as Hepburn napping at home with a fawn in her lap.
"I was there to make the women look as beautiful, the men as handsome and the movies as interesting as possible," Willoughby said in 2003 in the Times of London. "Beyond that, I photographed what appealed and was exciting to me."