ON 27 MAY 1967, Australians voted in favour of two amendments to the Australian Constitution that (1) empowered the Australian Government to make laws for all Australians, including aboriginal Australians and (2) included aboriginal Australians in the census or population count.

The amendments became law on 10 August 1967.

http://www.naa.gov.au/collection/fact-sheets/fs150.aspx

Each year, Australia celebrates National Reconciliation Week from 27 May to 3 June.