Governors of the Australian colonies:
Governor of New South Wales – Somerset Lowry-Corry, 4th Earl Belmore
Governor of Victoria – Sir John Manners-Sutton
Governor of Queensland – Colonel Sir Samuel Blackall
Governor of Western Australia – Sir Benjamin Pine (appointed, but not sworn in), Sir Frederick Weld (from 18 September)
Governor of South Australia – Sir James Fergusson, 6th Baronet (from 16 February)
Governor of Tasmania – Charles Du Cane (from 15 January)
Premiers of the Australian colonies:
Premier of New South Wales – John Robertson
Premier of Victoria – James McCulloch (until 20 September), then John Alexander MacPherson
Premier of Queensland – Charles Lilley
Premier of South Australia – Henry Strangways
Premier of Tasmania – Sir Richard Dry (until 1 August), then James Milne Wilson (from 4 August)
9 January – The British clipper ship Thermopylae arrives in Melbourne, having sailed from London in the record time of 64 days.
5 February – A large gold nugget, named The Welcome Stranger, is found at Moliagul, Victoria.
5 February - George Goyder establishes a settlement of 135 people at Port Darwin.
3 March – William Lanne, known as "King Billy", the last full-blood Tasmanian Aboriginal dies. His body is secretly dismembered and his skull removed while in the morgue, and Dr William Crowther, future Premier of Tasmania, is suspected as the culprit.
5 March – The New South Wales government declares that Saint Patrick's Day, St. Andrew's Day and St George's Day are no longer public holidays.
24 March – A fatal case of cholera is reported in Sydney.
8 May – The bushranger Captain Moonlite holds up a bank in Mount Egerton, Victoria.
22 June – Prince Alfred College opens in Adelaide, South Australia.
18 October – The Lithgow Zig Zag Railway was opened.
Science and technology
1 May – A submarine telegraph cable is completed, joining Tasmania to the mainland.
2 November – Warrior wins the Melbourne Cup.
20 January – F. Matthias Alexander, actor (died 1955)
21 February – Ernest Roberts, politician (died 1913)
10 March – John Longstaff, war artist (died 1941)
23 March – William Robson, politician (died 1951)
11 April – John Patrick McGlinn, soldier (died 1946)
13 April – Vida Goldstein, feminist and politician (died 1949)
27 April – May Moss, feminist and suffragette (died 1948)
2 May – Florence Stawell, classical scholar (died 1936)
14 May – Percy Abbott, soldier and politician (died 1940)
15 May – John Storey, Premier of New South Wales (died 1921)
18 May – Harold William Grimwade, soldier (died 1949)
19 May – William Gibson, politician (died 1955)
23 May – George Beeby, judge, politician and author (died 1942)
11 July – Peter McAlister, cricketer (died 1938)
21 July – John McDonald, politician (died 1934)
6 August – Marie Pitt, poet (died 1948)
7 August – E. J. Brady, poet (died 1952)
8 August – George James Coates, artist (died 1930)
28 August – Albert Fuller Ellis, prospector (died 1951)
28 September – John Hutton Bisdee, soldier and Victoria Cross recipient (died 1930)
24 October – Charlie McLeod, cricketer (died 1918)
30 September – Ernie Jones, cricketer (died 1943)
7 December – Frank Laver, cricketer (died 1919)
13 December – John Shirlow, artist (died 1936)
21 December – Albert Green, politician (died 1940)
29 December – Bill Howell, cricketer (died 1940)
3 March – William Lanne, Tasmanian Aboriginal (born 1835)
6 May – Henry Vincent, first superintendent of Rottnest Island Aboriginal Prison (b. c. 1796)
9 May – John Plunkett, Attorney-General of New South Wales (born 1802)
16 June – Charles Sturt, explorer (born 1795)
4 September – John Pascoe Fawkner, pioneer (born 1792)
6 November – Charles Flaxman, chief clerk of South Australia (born 1806)