With 88% of the vote counted, the Australian Electoral Commission said the Liberal/National coalition was heading for a landslide win, leading in 89 seats in the 150-seat House of Representatives, to Labor's 56.
Abbott, a former trainee Catholic priest, boxing enthusiast and monarchist, capitalised on the infighting in which Rudd ousted Julia Gillard as the Labor leader in June, three years after she did the same to him.
After six years of Labor rule, the country's 14.9 million voters have opted for a conservative government that has pledged to abolish unpopular carbon and mining taxes.
Rudd conceded defeat on Saturday evening.
"I wish his government well for the great and difficult challenges that lie ahead for Australia," Rudd, 55, told Labor supporters in Brisbane. "I gave it my all, but it was not enough for us to win."
Abbott, 55, won power after spearheading the attack on Labor's stewardship of the $1.5-trillion economy and its own infighting.
"I declare that Australia is under new management and is once again open for business," he told cheering supporters at a luxury hotel in Sydney.
"I now look forward to forming a government that is competent, that is trustworthy, and which purposefully and steadfastly and methodically sets about delivering on our commitments to you, the Australian people."
Abbott now faces the challenge of governing as the China-led mining investment boom wanes, crimping tax revenue and driving up unemployment.
"Abbott comes to power at a time when elevated downside risks plague the economy, threatening revenue forecasts and putting pressure on the deficit," said Katrina Ell, an economist at Moody's Analytics in Sydney.
"It's a hard sell cutting spending when the economy is slowing and needs help transitioning away from mining investment-led growth."
Abbott saw his popularity rise during the five-week campaign, vowing to repeal Labor's carbon price mechanism and mining profits tax.
Rudd struggled to convince voters he should be elected as three years of infighting and policy reversals damaged perceptions of Australia’s oldest political party.
"The clear take-out from this definitely is that disunity is death and we are not disciplined enough," said Labor Health Minister Tanya Plibersek.
Mike Williams, 66, a retired financial consultant, was among those who switched their vote from Labor in the last election to the coalition this time.
"We could do with a change," he said as he exited a polling station in Sydney’s Central Business District.
Erin Miller, 30, an executive assistant in the non-profit sector, said she also switched allegiances after voting for Labor in the previous two elections.
"I don’t particularly like Tony Abbott, but I don't think the Labor party has done a good job over the past few years," she said.
The election winner will be responsible for an economy that has avoided consecutive quarters of contraction - the local definition of a recession - for 22 years.
Signs of a slowdown have emerged, with interest rates cut to record lows to counter rising unemployment, forecast by Treasury last month to reach a more than decade-high 6.25% next year, as a China-led resources-investment boom fades.
The coalition, whose last term in office ended in 2007 after nearly 12 years, is pledging to cut taxes while funding a A$5.5 billion ($5 billion) per year maternity-leave programme.
It plans to cut red tape; reduce the civil service by at least 12,000 positions; lower subsidies for automakers; cancel handouts to parents of school children and achieve a budget surplus equal to 1% of gross domestic product within a decade.
"This is probably a verdict not so much on Rudd-Gillard personally, but I think it is a verdict on six years where there’s been division and there's been disunity," Liberal Senator Arthur Sinodinos said on ABC.