Ms Churcher, who was director of the National Gallery of Australia (NGA) from 1990 to 1997, was the first and so far only female director of the NGA.
She was known as Betty Blockbuster as a result of the large-scale exhibitions of famous European artworks she organised during her time at the NGA.
Before that, she was director of the Art Gallery of Western Australia.
She continued to promote Australian and international art to the public in later years, with a series of popular television programmes.
NGA director Gerard Vaughan described Ms Churcher as a "towering figure in the Australian art community".
"She will always be remembered here with deep affection for her tireless promotion of our visual culture, including her role as a popular presenter on TV, and I am reminded daily of her contribution to the nation," he said in a statement released by the gallery.
Ms Churcher was born in the Queensland city of Brisbane in 1931 and discovered art when her father took her to the Queensland Art Gallery as a child.
"It was like stepping on a magic carpet because off I went!" she once said in an interview.
In recent years, declining eyesight made it increasingly difficult for her to look at the paintings she loved.
In an interview with the Australian Broadcasting Corporation several years ago she said that when she realised she could no longer remember the paintings in the Prado and the National Gallery that she adored, she decided to tour the great galleries of Europe, sketch the masterpieces and commit their details to memory.
"The paintings that I most like are the ones that demand a second, and a third and a fourth look," she said.
"And each time you look, they've got something more to give you.
"I know that I could look at Velazquez's Maid of Honour until I died and I still couldn't get to the bottom of it, to find out how it was that he did it."
Ms Churcher was married to artist Roy Churcher, who died last year. She died on Monday night surrounded by her four sons.
Betty Churcher, one of Australia's most popular and innovative arts administrators, has died aged 84.