The annual rise in gross domestic product, included in the Australian Bureau of Statistics' quarterly national accounts release on Wednesday, was above the expectations of economists and the Reserve Bank of Australia.
The central bank had forecast the economy to grow by 1.6 per cent in the 12 months to June.
The annual economic growth rate climbed from the upwardly revised 1.4 per cent pace recorded in March.
Treasurer Jim Chalmers said Australia's economy was gathering momentum in the face of global economic uncertainty.
"This is a welcome and substantial pick-up in growth," he said in a statement.
"Today's very welcome numbers confirm the private sector recovery we've been planning and preparing for is gathering pace."
Private demand contributed 0.5 percentage points to GDP growth, mainly through higher household consumption.
Public demand had no impact on growth as a rise in government spending was offset by a fall in public investment .
ABS head of national accounts Tom Lay said the previous quarter was impacted by weather events.
Domestic final demand was the main driver of growth, led by household and government spending, while public investment was the largest detractor from growth.
"End of financial year sales and new product releases contributed to rises in discretionary spending on goods including furnishings and household equipment, motor vehicles and recreation and culture goods," Mr Lay said.
On a quarterly basis, the nation's economy grew by 0.6 per cent.
Australia avoided dropping back into a per capita recession.
GDP growth per capita was up 0.2 per cent per person, after a drop of 0.2 per cent on a per capita basis the previous quarter.
It's only the second quarter out of the past 10 that each Australian has seen an increase in their share of GDP - a crude measure of household living standards, because it accounts for growth in the size of the population.
The household saving ratio fell from 5.2 per cent to 4.2 per cent, amid a rise in disposable income.
"Consumption is growing because real incomes are growing. Under Labor, people are earning more and keeping more of what they earn," Dr Chalmers said.
The quarterly economic pulse check comes after the RBA cut interest rates for a third time this year in August, which is expected to boost growth as borrowers gain greater purchasing power.
Minutes from the meeting revealed the central bank's board expected the recovery in GDP growth to be more gradual than previously forecast, amid more subdued public demand.
Following the release, the Australian dollar and government bond yields surged, while equities fell, as traders reined in expectations for more rate cuts.
Inflation spiked unexpectedly in July, although the Reserve Bank takes its guidance from the less volatile quarterly figures, which are expected to show inflation remains subdued when next updated in late October.
But combined with Wednesday's GDP figures, they indicate the economy is running hotter than previously thought, reducing the urgency for the RBA to lower rates.
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