US President Donald Trump tweeted his congratulations to Prime Minister Scott Morrison after his "miraculous" election victory.
The coalition is approaching the 76 seats it needs to have a majority in the Australian parliament, with 74 at the end of the Saturday night count, after a result that defied months of opinion polls that consistently showed Labor.
The result was applauded by conservatives in the United States and compared to President Trump's 2007 presidential surprise when polls predicted he would lose.
"Congratulations to Scott for a GREAT VICTORY!" the president of the United States tweeted Sunday morning, Australian time.
Earlier, US cable news channel Fox News described the Australian Prime Minister's victory as "an extraordinary victory".
The American political activist Pamela Geller trumpeted "the people are recovering their countries from the totalitarian left".
"SHOCKING Election results in Australia: the Australian Conservative party takes the extraordinary victory: the Trump effect. The polls were wrong …. again," Ms Geller, founder of The Geller Report, wrote on Twitter and president of Stop Islamization of America.
Axios Amy Harder told readers that the result of the election indicates that "Australia will continue to follow closely the positioning of the Trump administration on climate change.
"The climate advocates said that these elections would be a referendum on current leadership positions on climate change, the results suggest that both voters do not care so much about the issue over others or prefer less aggressive measures, since the "current leadership is pursuing", wrote Ms. Harder.
The New York Times described how "the conservative victory also adds Australia to a growing list of countries that have moved to the right through the politics of resentment, including Brazil, Hungary and Italy.
"Mr. Morrison has launched mixed smiles and scaremongering, especially warning the old voters and rural voters that a left-wing government would leave them behind and favor the condescending elites."
The pre-election polls had hinted that the ALP would win the federal election and the leader Bill Shorten would be the next prime minister.
"I've always believed in miracles," Morrison told the fans Saturday night.