Tony Abbott: "From today I declare that Australia is under new management"
In pictures: Australia votes
Key policy battlegrounds
Why boat people risk it all
Is the economy on track?
Australia's opposition has crushed the governing Labor party in a general election that has returned the Liberal-National coalition to power for the first time in six years.
Early projections show Labor winning 55 seats compared with the coalition's 91.
Liberal leader Tony Abbott said he looked forward to forming a competent and trustworthy government.
Prime Minister Kevin Rudd earlier admitted defeat and said he would not stand again for the Labor leadership.
The main election issues were the economy, reducing the number of asylum seekers arriving by boat, and a tax on carbon emissions.
Mr Rudd called the election after defeating Julia Gillard in a leadership challenge in June, amid dismal polling figures that showed Labor on course for a wipe-out.
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Leader of Liberal Party and main opposition Liberal-National coalition
Born 1957 in UK to Australian parents
Rhodes scholar, former student boxer and Catholic priest trainee
Held employment and health and ageing portfolios in Howard government
Profile: Tony Abbott
Under Mr Rudd, Labor initially saw its figures improve. But Mr Abbott, who enjoyed the strident support of Rupert Murdoch's newspapers, then widened the gap again.
"From today I declare Australia is under new management and Australia is now open for business", Mr Abbott told a cheering crowd as he delivered a victory speech.
He said that he would put the budget back into surplus, and boats bringing migrants from Asia would stop.
He added that support for Labor was at its lowest ebb for 100 years, and said the results showed that the Australia people would punish anyone who took them for granted.
Mr Rudd said he had phoned Mr Abbott and wished him well.
"I gave it my all but it was not enough for us to win," he said. But he was pleased that Labor was preserved as a "viable fighting force for the future".
Mr Rudd retained his seat in the Brisbane constituency of Griffith but said he would not re-contest the Labor party leadership because the Australian people "deserve a fresh start".
"I know that Labor hearts are heavy across the nation tonight. As your Labor leader I accept it as my responsibility," he said.
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Australians have cast their ballots in a general election that brought to an end six years of Labor government.Continue reading the main story
With two-thirds of the votes counted, the Australian Broadcasting Corporation said the coalition had secured 85 seats in parliament and was on course to win 91. Labor had secured 54, with a predicted final tally of 55.
In the previous parliament, Labor relied on the support of independents and the Greens for its minority government, with 71 seats to the coalition's 72.
Mr Abbott took on the leadership of the flagging Liberal-National coalition in 2009.
A Rhodes scholar who once wanted to be a Roman Catholic priest, Mr Abbott has pledged to repeal both the mining and carbon taxes introduced by Labor.
He has also promised a raft of budget cuts, including reducing the foreign aid budget by A$4.5bn ($4bn, £2.6bn).
But he says he will fund an expanded paid parental leave scheme.
AnalysisJon DonnisonBBC News, Sydney
Labor's six years in power are emphatically over. Australia's economic growth during difficult global financial times should have played well for an incumbent government. But the economy has begun to slow and Kevin Rudd's Labor party has been undone by disunity and infighting. The rivalry between Mr Rudd and Julia Gillard which saw the leadership of the party and the country switch back and forth did not sit well with voters.
You sense from voters that Mr Abbott's victory is not so much a ringing endorsement as a rejection of Labor. He's a conservative who has promised a tough line on immigration and asylum-seekers. He opposes gay marriage and has been a sceptic on climate change. Kevin Rudd sold himself as the comeback kid. It didn't work. His party now faces a period of further introspection.
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The economy has been at the heart of campaigning.
Mr Abbott will be charged with managing the transition as the mining and resources boom subsides, amid slowing demand from China and slumping commodity prices.
Ahead of the polls, his coalition highlighted bitter Labor infighting, seeking to portray itself as the more stable party.
And former Labor Prime Minister Bob Hawke blamed the internal divisions for Labor's defeat.
"I really believe this was an election that was lost by the government rather than one that was won by the opposition," he said.
Julia Gillard, meanwhile, congratulated the Labor candidate who succeeded her in her seat, as she bowed out of politics.
And in something of an upset, billionaire Clive Palmer - who founded the fringe Palmer United Party - appeared on course to win a seat in parliament.
More than 14 million people were expected to vote in Saturday's election. Voting is compulsory in Australia.
Polling closed in eastern states at 18:00 (08:00 GMT) and in Western Australia two hours later.