Germany-born Faas won four major photo prizes, including two Pulitzers, during his career, and served as AP's Saigon photo chief at the height of the war.
In Saigon he trained and mentored young Vietnamese photographers who captured many of the war's defining images.
Faas was injured in 1967 and later used a wheelchair for many years.
He died after suffering years of health problems, including paralysis from the waist down.
"Horst Faas was a giant in the world of photojournalism whose extraordinary commitment to telling difficult stories was unique and remarkable," said Santiago Lyon, AP's global head of photography.
"He was an exceptional talent both behind the camera and editing the work of others and even in the grimmest circumstances he always made sure to live life to the fullest," Lyon said.
"He will be sorely missed by scores of colleagues, especially that reduced group with whom he covered conflict, particularly the Vietnam generation."
Speaking to the BBC in 2007, Faas described his job in simple terms.
"I tried to be in the newspapers every day, to beat the opposition with better photos. I didn't try to do anything grandiose. The photos were used and published and asked for, becuase Vietnam was on the front pages year after year after.
"I lived from day to day, from event to event. It was a perfect story for an agency photographer."
He began his career covering conflicts in 1960, four years after joining the Associated Press (AP).
He worked in what was then Zaire, and in Algeria, before relocating to Vietnam, where he won his first Pulitzer Prize in 1965.
Accepting the award, he said he aimed to "record the suffering, the emotions and the sacrifices of both Americans and Vietnamese in... this little bloodstained country so far away," AP said.
He had a front row view of much of that suffering.
When not in the midst of the conflict, Faas worked at AP's Saigon base, viewing and selecting images from his photographers to transmit on the wire to the rest of the world.
Under his direction, AP photographers captured images that quickly became synonymous with the long war: among the most notable were Eddie Adams' image of the execution of a Viet Cong suspect and Nick Ut's picture of a naked Vietnamese girl fleeing a napalm attack.
Despite being injured in 1967, he stayed in the country until 1970.
"I don't think anyone stayed longer, took more risks or showed greater devotion to his work and his colleagues," said New York Times journalist David Halberstam, who once lived with Haas.
"I think of him as nothing less than a genius."

The US sprayed 12 million gallons of the defoliant over jungles between 1961 and 1971 during the Vietnam war.
Vietnamese experts say more than three million people have suffered the effects of the herbicide, of which some 400,000 died.
The development is being hailed as one of the most significant in relations between Washington and Hanoi.
A ceremony to launch the programme was held at the Danang airport where the defoliant was stored before being sprayed over forests hiding fighters from the Viet Cong, guerrillas backed by the Communist government of North Vietnam.
US-Vietnam ties have blossomed since diplomatic relations were established 16 years ago and steps to resolve issues left over from the war have formed a cornerstone of progress, say correspondents.
"I think it's fair to say that dioxin contamination and Agent Orange was one of the single most neuralgic issues in the US-Vietnam relationship," said US charge d'affaires Virginia Palmer.
For years, Hanoi and Washington argued about questions of compensation for victims of the defoliant.
But now the US recognises that dioxin, found in Agent Orange, is a highly toxic substance.
"Studies suggest that this chemical may be related to a number of cancers and other health effects in humans", says the US Department of Veterans Affairs.
Five years ago the embassy began to shift the focus to cleaning up dioxin hot spots, clearing the path for swift progress on what had become the biggest remaining war-era issue.
The US Congress appropriated an initial $3m (Â£1.8m) in 2007 for the effort and the figure has since risen to $32m.
Celebrated combat photographer Horst Faas, who covered the Vietnam War for the Associated Press, has died aged 79, his daughter says.
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Vietnam and the United States have taken the first step towards cleaning up Agent Orange contamination.