CBS announced his death, but the cause was not immediately known.
The Canadian-born Mr. Safer spent more than 50 years as a CBS News correspondent.
In August 1965, Safer's report that showed American servicemen torching a Vietnamese village to the ground despite encountering no resistance from residents ignited a firestorm in the US. He joined CBS News in 1964 as a London-based correspondent and eventually became the London bureau chief.
Over the course of his prestigious career, Safer was awarded 12 Emmys, three Peabody Awards and the Lifetime Achievement Emmy from the National Academy of Television Arts and Sciences.
Colbert said the first time he met Safer was for his own "60 Minutes" profile while he was hosting "The Colbert Report". "I said, 'Morley, you look like you're from the future', and he said, 'Stephen, I am the future, ' and got off the elevator".
Safer's reporting from Vietnam in the 1960s, which angered many, was considered groundbreaking.
CBS chairman and CEO Leslie Moonves said Safer broadly impacted the news industry: "Morley was one of the most important journalists in any medium, ever".
Safer's expose ignited a firestorm, with President Lyndon Johnson giving CBS President Frank Stanton a tongue-lashing.
He quickly became a fixture at "60 Minutes" - and part of that show's rough-and-tumble behind-the-scenes culture as the stature and ratings of the show took off.
CBS said Safer changed war reporting forever with his work in Vietnam before becoming an "iconic" correspondent who was one of US television's most enduring stars. He was 84 years old and had recently announced his retirement from his homebase of almost half a century, the CBS Sunday news magazine60 Minutes.
"Mind if I smoke?"