"John Olsen leaves a space but true to form, he saw to it that it would be filled with colour and light as bright as that twinkle in his eye," Anthony Albanese said at the service in Sydney.
Olsen's career spanned almost seven decades and he died on April 11, aged 95, still painting in the final weeks of his life.
One of few people to have won each of the Wynne, Sulman and Archibald prizes, he was also appointed Officer of the Order of Australia and the Order of the British Empire.
Australia's art world paid tribute to the painter on Monday, with Wendy Whiteley, Ken Done and Ben Quilty among those in the crowd at the Art Gallery of NSW.
Daughter Louise remembered how the Olsen family lived in a mudbrick house with paintings by some of Australia's greatest artists on the wall, and she felt proud her father was unlike any other.
Cooking was at the heart of the family, she said, and the sale of a painting would be celebrated with paella and champagne.
Tim Olsen said his father showed them that a different world was possible.
"We want to keep that vision and that dream alive... especially in times like today, in such a difficult world, we have to take refuge in beauty."
Friend and master of ceremonies at the service, Michael Yabsley, said Olsen brought untold joy to many and had charisma by the truckload, even in his later years.
"When it came to lighting up a room he was in a class of his own - remarkably, in the twilight of his life, John was still in the prime of his life," he said.
He remembered the artist as a bon vivant, a cook, philanthropist, teacher, mentor, lover of literature, and businessman too.
"The great man would say the only embellishment to an outstanding piece of art should be a red dot."
One of Olsen's grandchildren, Georgia Blake, read from the Kenneth Slessor poem Five Bells, which inspired one of the painter's best-known works, which was installed at the Sydney Opera House.
A video montage showed black and white footage of Olsen working energetically on a canvas and clips of him showing Salute to Five Bells to Queen Elizabeth II at the opening of the Opera House in 1973.
He was clearly having a tremendous time.
Last of all were projections of his paintings lighting up the iconic building for the 2023 Vivid festival.
The Sydney Art Quartet played some of Olsen's favourite pieces of music and musician William Barton performed his piece Spirit of the Landscape for voice and didgeridoo.
"Now Uncle John is up there painting those big dreaming stories too with those elders of our landscape and our mother country... his paintbrush was his message stick," Barton said.
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