Gleeson attended the East Sydney Technical College (1934-36), exhibiting early Surrealist works at the Contemporary Art Society in Melbourne in 1938. In 1941 he delivered his treatise, The Necessity for Surrealism, advocating ‘the real anarchy of thought,’ and maintaining that this was a means to liberate humanity from the constraints of reason. In his paintings and prints, Gleeson was influenced by Spanish Surrealist Salvador Dali (1904-1989), creating hallucinogenic landscapes in which forms and objects were in a perpetual state of biomorphic transformation.
In addition to painting, Gleeson was also an art critic for the Sydney Sun (1949-72) and the Sydney Morning Herald (1962-72) as well as the author of books on Australian art, including a monogram on William Dobell. Acknowledged for his contribution to Australian art, Gleeson was made an Officer of the Order of Australia in 1990. His work is held in the Art Gallery of South Australia, Adelaide and the National Gallery of Victoria, Melbourne.