The opposition Labor Party, meanwhile, has begun the search for a new leader after Bill Shorten stepped down following the defeat in a poll which had been seen as unlosable for his party.
By the time just over 75 per cent of votes had been counted, the coalition had won 73 of the 76 seats needed to form a majority government, according to calculations from the Australian Broadcasting Corp.
The government had gone into the election as a minority government, with just 73 seats.
And it was possible the coalition would again have to govern in the minority, relying on agreements with independent and minor party lawmakers to transact government business.
Scott Morrison celebrated his win by heading to church in Sydney on Sunday morning, and was later seen surrounded by fans after arriving to watch his team, Cronulla Sharks, in a rugby league match.
Thanking Australians for returning him to office, he said: “I give thanks to live in the greatest country in all the world. Thanks again to all Australians all across the country.”
The 51-year-old, who received a congratulatory phone call from US president Donald Trump, said he was eager to return to work on Monday to form his new government.
He had told supporters late on Saturday, who had earlier seemed resigned to defeat, that he had always believed in miracles.
Centre-left Labor, which has governed Australia for only 38 of its 118 years as a federation, was rated an overwhelming favourite to topple the conservative Liberal-National coalition government after its six years in power.
Opinion polls in Australia had all pointed to a Labor victory – and one betting agency even paid out AU$1.3m (£700,000) to those who backed Labor to win just days before the election.
As Labor absorbed the defeat, deputy leaders Tanya Plibersek and Anthony Albanese told reporters they were considering running for the party’s leadership.
Agencies contributed to this report.