Green’s work is represented in over seventy major public and private collections, including the collections of the Museum of Modern Art and the Solomon R Guggenheim Museum, New York; the Corcoran Gallery of Art, Washington DC; the Museum of Contemporary Art, Chicago; the Albertina, Vienna; the Museum of Contemporary Art Australia, Sydney; the Art Gallery of New South Wales, Sydney; the UQ Art Museum, Brisbane; the Heide Museum of Modern Art, Melbourne; and the National Gallery of Australia, Canberra. 

In 2007 Green was awarded the Order of Australia, one of the nation’s highest honours.