See also: 1938 in Australia, other events of 1939, 1940 in Australia and the Timeline of Australian history.
- 13 January – The bushfires of Black Friday kill 70 people in Victoria.
- 27 March – The first CAC Wirraway training aircraft, A20-3, takes to the air at Fishermans Bend, Victoria.
- 7 April – Prime Minister Joseph Lyons dies of a sudden heart attack, the first Prime Minister to die in office. Sir Earle Page, the leader of the Country Party is appointed caretaker Prime Minister until the United Australia Party can elect a new leader.
- 26 April – Robert Menzies is elected leader of the United Australia Party, and is sworn in as Prime Minister.
- 10 June – Premier of Tasmania Albert Ogilvie dies in office. Edmund Dwyer-Gray acts as Premier until he is officially elected as leader of the Labor Party in Tasmania on 6 July.
- 3 September – World War II begins. Australia declares war on Germany, following the United Kingdom and British Dominions' declaration of same, after the German invasion of Poland.
- 15 September – Robert Menzies announces a new War Cabinet.
- 1 December – Australia agrees to take 15,000 Jewish refugees fleeing Europe, following the German occupation of Austria and Czechoslovakia.
- 18 December – Edmund Dwyer-Gray steps aside as Premier of Tasmania, by prior arrangement with Robert Cosgrove to assume the premiership.
Arts and literature
- 6 January – Murray Rose, swimmer
- 29 January – Germaine Greer, academic and feminist
- 13 February – Andrew Peacock, politician
- 13 February- Allan Pearson, Australian Farmer and Rural Businessmen
- 5 March – Tony Rundle, Premier of Tasmania (1996–1998)
- 4 April – Alex George, botanist
- 7 April – Brett Whiteley (died 1992), artist
- 12 April – Johnny Raper, Australian rugby league footballer
- 20 April – Elspeth Ballantyne, actress
- 12 May – Reg Gasnier, Australian rugby league footballer
- 12 July – Phillip Adams, broadcaster and writer
- 26 July – John Howard, Prime Minister of Australia (1996–2007)
- 5 September – George Lazenby, actor (James Bond)
- 8 October – Paul Hogan, comedian and actor
- 9 October – John Pilger, journalist and filmmaker
- 10 October – Clive James, writer and social commentator
- 25 November – Ian Smith, politician
- 26 December – Fred Schepisi, film director
- 14 February – James Webb, NSW politician
- 9 March – Edwin Greenslade Murphy (born 1866), journalist and poet
- 7 April – Joseph Lyons (born 1879), Prime Minister of Australia (1932–1939) and Premier of Tasmania (1923–1928)
- 25 April – Sir Charles Powers (born 1853), High Court judge
- 10 June – Albert Ogilvie (born 1890), Premier of Tasmania (1934–1939)
- 6 August – James MacCallum Smith (born 1868), WA politician
- 30 August – Edward Sydney Simpson (born 1875), mineralogist and geochemist
- 3 October – Henry Augustus Ellis (born 1861), physician and federalist
- 22 October – Sir John Langdon Bonython (born 1848), politician and journalist
- 15 November – William Hill (born 1866), politician
- 6 December – Sir Ernest Scott (born 1867), historian