The Seekers hold the record for the biggest concert crowd in the southern hemisphere, with about 200,000 people attending a show in March 1967.
They were named joint Australians of the Year in 1967.
Durham eventually left the group and had a successful solo career, though she continued to reunite with The Seekers over the years.
The Seekers members were each honoured as Officers of the Order of Australia in 2014.
Durham's bandmates took to social media to share a tribute to her "magnificent musical legacy".
"Our lives are changed forever losing our treasured lifelong friend and shining star," they said.
"Her struggle was intense and heroic — never complaining of her destiny and fully accepting its conclusion.
Her sister Beverley Sheehan also spoke of the closeness they shared.
"Judith's joy for life, her constant optimism, creativity and generosity of spirit were always an inspiration to me," she said.
Durham's family has asked for privacy at this time.
Federal Minister for the Arts Tony Burke said Durham was "once, the best known Australian voice ".
"With The Seekers and solo, Judith earned her place as an icon of our music," he said.
"In 1967, 10 per cent of the Melbourne population attended a single gig.
"What a contribution. What a loss. I am Australian will be played forever. RIP."
Entertainer Anthony Callea posted: "The skies above just gained a voice of an angel."
