The painter, known for changing the way people viewed the Australian landscape, died peacefully on Tuesday evening at his home in the NSW southern highlands surrounded by his family.
Born in Newcastle, Olsen's career spanned more than 60 years, with his work exhibited in galleries across the nation and overseas.
He was a giant who never lost the twinkle in his eye, Prime Minister Anthony Albanese said in an online statement on Wednesday.
"A man of talent, charisma, generosity and humility, he was a poet of the brush, a truly great explorer and interpreter of the Australian landscape. We were so lucky to have him," he said.
Olsen won the country's major art awards across almost 40 years, including the Archibald, Wynne and Sulman prizes.
His children Louise and Tim Olsen said their father was a bon vivant and raconteur known for his quick wit and rakish beret.
"Our father was a titan of the art world and beloved by many in Australia and overseas but to us he was Dad, in all the wonderful humaneness, complexity and humanity that word encapsulates," they said in a statement released on Wednesday.
John Olsen was still painting in his studio on Saturday, just days before he died.
"Painting was our father's life, and he was painting right up to the last in his studio, with friends calling in to see him which he always loved," his children said.
Among the artist's acclaimed works is Salute to Five Bells, which hangs inside the Sydney Opera House, and a tribute to his long career will be beamed onto the building's sails next month during the Vivid Sydney festival.
Just weeks ago, the artist had planned to watch the light show from a plush Sydney hotel room surrounded by his family as a kind of last hurrah.
"What better way to say goodbye?" he told his children.
But Olsen was able to watch an animation of the Opera House projection in the days before he died, which his son said brought him to tears.
The painter spoke to AAP last year about his affinity with rural and remote Australia, having long captured its wild terrain.
"To be an Australian landscape painter is to be an explorer," he said after donating several of his works to a regional NSW gallery.
"There is so much to look at and observe about the Australian landscape, how it varies from tropical to the coastal fringe and the interior.
"It's so multiple. It's a beautiful animal, that landscape."
After receiving an Order of Australia in 2001, Olsen described art as a form of compulsion, which he started developing at age four.
"Artists are born, not made," he said.
He won the Archibald for Self-portrait Janus-Faced in 2005, the Wynne Prize for The Chasing Bird Landscape in 1969 and A Road to Clarendon: Autumn in 1985, and the Sulman Prize for Don Quixote Enters the Inn in 1989.
Olsen received numerous other awards in his long career, including an OBE in 1977.
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