Born in Canada, he lived in New York and only recently announced his retirement.
During his six decades of reporting, Safer won hundreds of awards, including a dozen Emmys and three Peabody Awards.
He is survived by his wife and daughter.
Just this past Sunday, "60 Minutes" said goodbye to Safer in a tribute marking the close of a 61-year career.
During the hour-long show, Safer was described as tough, funny, intrepid, curious and courageous, with reporting that ranged from the Cold War to cyberspace, from the Muppets to the Orient Express.
"He's asking a question on behalf of all of us," said "60 Minutes" executive producer Jeff Fager.
Safer's first report on "60 Minutes" in 1970 was about the training of U.S. Sky Marshals. His 919th and last, a profile of Danish architect Bjarke Ingels, was broadcast in March. At 84 and dealing with health issues, Safer had cut back on work in recent years. The Toronto-born Safer was the first Saigon bureau chief for CBS News.
"Morley was right in back of me every step of the way. I had to do it. He didn't," recalled a former Army soldier whose unit Safer joined for a story. Slogging through the jungle with bullets sometimes flying was tough and dangerous duty, but "Morley was cool as a hog on ice."
His 1965 report on U.S. Marines burning the Vietnamese village of Cam Ne was a turning point in public attitude toward the war. An outraged President Lyndon Johnson wanted him fired.
Safer broadcast a report from inside China in 1967 when it still was largely a closed society and, as a Canadian Broadcast Corp. reporter, witnessed the building of the Berlin Wall in Germany in 1961.
He was a London bureau chief for CBS News in the late 1960s before joining "60 Minutes."
Safer considered one element above all - the spoken word - to be essential for great television: "What you're aiming at," he said, "are people's ears rather than their eyes."
A focus on language over video might sound strange for a journalist so identified with TV.
"I really don't like being on television. I find it intimidating," he confided, but added he had long ago made peace with it, explaining with a sly smile, "the money's very good."
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The Associated Press contributed to this report. null