Post world war 2 immigration is considered the third of the major migration phases in Australia's post First Fleet in 1788, according to [the Melbourne Immigration Museum][1]

> We focus on four periods: the gold rush days of the 1840s to 1900,
> Federation to the end of the Second World War, then post-war to the
> early seventies, and finally 1973 to the present day.

In 1945, Arthur Caldwell, Australian Minister for Immigration declared

> Australia wants, and will welcome, new healthy citizens who are
> determined to become good Australians.

[The Migration heritage website also states][2]

> After World War II ended in May 1945 Europe was in chaos. Germany was
> crushed and the map of Europe was being carved up by the United States
> and the Soviet Union. Western Europe was supported by the United
> States while Eastern Europe was invaded by the Soviet Union. Migrants
> began streaming out of Eastern Europe to places like Australia and the
> United States to get away from the oppression in their homelands by
> the Soviet Union. The Cold War between the United States and the
> Soviet Union meant that nuclear war was a real threat and some people
> saw Australia as a safe place to live.

[The Australian government says][3]

> After the Second World War (1939–45) the Australian government
> committed to a vigorous and sustained immigration program. The purpose
> of this ambitious program was to meet labour shortages, protect
> Australia from external threat and create prosperity. As a result,
> from 1945 to 1975 Australia's population almost doubled from 7½
> million to 13 million. About 3 million migrants and refugees arrived.
> 
> This was a major break in policy. It was not the support for
> immigration that was new, as Australia had been supporting immigration
> since its inception and accepting refugees since the 1830s. Indeed,
> Australian society was characterised by an expanded migration of
> people, especially men from southern Europe, the Adriatic and the
> Mediterranean in the years prior to the Second World War. This
> migration had contributed to the making of modern Australia.
> 
> However, in July 1947, the Australian Government entered into an
> agreement with the new International Refugee Organisation to settle
> displaced people from camps in Europe. The difference between a
> migrant and a refugee is explained by UNHCR, the UN Refugee Agency:
> Note that this was absolutely still under the White Australia policy,
> so covered

Note this was still under the White Australia policy

> After the Second World War, the Australian government assumed that its
> main source of immigrants would be Western Europe, but half the
> immigrants in the 1950s and 60s were from the European continent. In
> these two decades, Australia welcomed large groups of people, mostly
> from Eastern Europe: Poland, Yugoslavia, Latvia, Lithuania, Estonia,
> Ukraine, Czechoslovakia and Hungary. The overwhelming majority of
> refugees were Eastern Europeans fleeing persecution in Soviet Bloc
> countries.

Which ended in 1972 under Gough Whitlam

> From the mid-1970s the policy changed again. Mass migration programs
> for British and European immigrants ended, the remnants of the White
> Australia Policy were abolished, and arrivals began to come from
> countries closer to Australia. At the same time political and
> community support for immigration weakened and the catchcry 'Populate
> of Perish' [sic!] lost favour.

Disclaimer: I'm an immigrant to Aus myself. Though phase 4.

  [1]: https://museumvictoria.com.au/immigrationmuseum/whats-on/getting-in/
  [2]: http://www.migrationheritage.nsw.gov.au/exhibition/objectsthroughtime-history/1945-1965/
  [3]: http://www.australia.gov.au/about-australia/australian-story/changing-face-of-modern-australia-1950s-to-1970s