He was born at St Kilda to civil engineer Edmond Francis Gleeson and nurse Bertha Anne Stephenson.
He became a rural property manager, and on 3 February 1940 married Phyllis Pullar, with whom he had three children.
During World War II he served with the Australian Electrical and Mechanical Engineers, and on his return became a farmer at Ettrick near Camperdown.
He was active in agricultural organisations, serving as president of the Victorian branch of the Australian Primary Producers Union and as federal vice-president.
A member of the Liberal Party, he was elected to the Victorian Legislative Council in a by-election for South Western Province in 1965, and served there until his retirement in 1979.