"The pen has run dry, its ink no longer flowing - yet Mr. Curly and his ducks will remain etched in our hearts, cherished and eternal," reads a statement posted on his Instagram account.
Leunig, as his cartoons and paintings were always signed during his six-decade career, died peacefully early on Thursday.
He was surrounded by his children and loved ones, as well as classical music and sunflowers, during his final days.
Michael Leunig was born in East Melbourne in June 1945, the second-eldest of five children.
He went to Footscray North Primary School and Maribyrnong High School, and cites Enid Blyton, Phantom comics, JD Salinger, The Beatles and Spike Milligan among his early influences.
He became a popular newspaper cartoonist since his first cartoon for The Age in 1969, publishing his first collection in 1974 and another 23 collections since.
He was declared a national living treasure by the National Trust in 1999 and has been awarded honorary degrees from La Trobe, Griffith and the Australian Catholic University.
Some of his cartoons sparked controversy over the years, and Leunig was let go by Nine's publishing division in August.
Writing about the end of his tenure on his website, Leunig said he was sad about what has become of newspapers, and that he was "disposed of" along with many others in a cost-cutting "media bloodbath".
"With some terrific exceptions, Australian mainstream cartoonists can't be so funny, spirited and naughty any more," he said.
Spectrum editor Lindy Percival paid tribute to Leunig's career when his final cartoon was published.
"Through Leunig's work, we have contemplated life's beautiful and occasionally baffling moments: Mr Curly arriving home to his curly-headed family; a simple soul dreaming of floating coloured petals; and a father and son watching the sun set on TV, oblivious to the real thing happening outside their window," she wrote.
