She presented a number of unscripted series for the BBC in the 1990s, including Sister Wendy's Odyssey and Sister Wendy's Grand Tour.
Another added: "Aw, sorry to hear Sister Wendy has died".
Wendy Beckett was born in South Africa, before moving to Edinburgh as a child and joining a convent at the age of 16.
Beckett began her art career as a magazine critic, reviewing exhibitions for small British art journals in the mid-1980s and published her first art book, "Contemporary Women Artists", in 1988.
It was at an art exhibition in Norfolk, where the BBC happened to be filming a documentary about Germaine Greer, that she was approached to give her impression of the show.
The author, Xinran Xue, who was a close friend, said her death was a "huge loss" for the art world. She stood in front of the paintings dressed in a black nun's habit and discussed the paintings without a script or teleprompter.
At its height, Sister Wendy's Odyssey, would regularly pull in four million viewers as she evaluated artwork.
She made her BBC presenting debut in 1991 with a documentary on Britain's National Gallery and went on to become a household name.
In 2007 Sister Wendy was asked by The Huffington Post about her support for same-sex couples, despite the church's opposition.
"Sister Wendy had a unique presentation style, a deep knowledge of and passion for the arts", BBC director of arts Jonty Claypole said. According to The New York Times, she attended mass daily.
JRR Tolkein tried to persuade her to stay on at Oxford as an academic, but she instead moved to Liverpool and then back to South Africa.
Former England cricketer and television presenter Phil Tufnell worked with Sister Wendy on the BBC's One Show. As an art historian she covered all subjects of art from sexuality, gender, nudity to social issues.