The following lists events that happened during 1837 in Australia.

Governors of the Australian colonies:

• Governor of New South Wales - Major-General Sir Richard Bourke
• Governor of South Australia - Captain John Hindmarsh
• Lieutenant-Governor of Tasmania - Captain Sir John Franklin
• Governor of Western Australia as a Crown Colony - Captain James Stirling

• 2 January - The Supreme Court of South Australia is established by Letters Patent, five days after the founding of the colony.
• 6 March - The Theatre Royal in Hobart opened. It remains Australia's oldest working theatre.
• 28 March - The Hoddle Grid of streets for the central business district is surveyed by Robert Hoddle.
• 1 June - First inner-city land sale in Melbourne.
• 10 June - The first whale is caught in Western Australia.

• 13 February – James Venture Mulligan, prospector and explorer (born in Ireland) (d. 1907)
• 26 February – William Hann, pastoralist and explorer (born in the United Kingdom) (d. 1889)
• 7 March – Gracius Broinowski, artist and ornithologist (born in the Russian Empire) (d. 1913)
• 16 March – Frederick Wolseley, inventor and woolgrower (born in Ireland) (d. 1899)
• 1 May – Ernest Henry, explorer and pioneer grazier (born in the United Kingdom) (d. 1919)
• 9 May – Ben Hall, bushranger (d. 1865)
• 9 August – John Atherton, explorer (born in the United Kingdom) (d. 1913)
• 26 November – Thomas Playford II, 17th Premier of South Australia (born in the United Kingdom) (d. 1915)

• 10 February – Frederick Goulburn, New South Wales politician and soldier (born and died in the United Kingdom) (b. 1788)
• 15 March – William Cox, soldier, explorer and pioneer (born in the United Kingdom) (b. 1764)
• 5 September – James Ruse, farmer and convict (born in the United Kingdom) (b. 1759)
• Unknown, possibly September – Francis Greenway, architect and convict (born in the United Kingdom) (b. 1777)
• Unknown – Joseph Gellibrand, explorer and lawyer (born in the United Kingdom) (b. 1792)