Prime Minister Tony Abbott says his government is determined to deliver on its promises to scrap the carbon tax, stop the asylum seeker boats and improve the federal budget.
Mr Abbott also said the coalition, which begins its first official day in office on Wednesday, expected to be judged on what it achieved, or didn't achieve.
"We pledge ourselves to serve the people of Australia for their benefit, to the very best of our ability," Mr Abbott said.
"We are determined to honour our commitments to scrap the carbon tax, to stop the boats, to get the budget under control and to
build the roads of the 21st century.
"We will be a problem-solving government based on values not ideology."
Mr Abbott was sworn in by Governor-General Quentin Bryce at Government House at about 10.30am (AEST) to become Australia's 28th prime minister.
His mother Faye and father Dick, wife Margie, daughters Louise, Frances and Bridget, and his sisters Christine Forster and Pip Abbott watched on.
Ms Bryce noted the "great responsibility" Mr Abbott was taking on and wished him well.
"Thank you so much, Excellency," Mr Abbott said.
Margie Abbott held his hand as official pictures were taken before give him a kiss on the cheek.
Mr Abbott then held his first executive council meeting with Ms Bryce, before attending the swearing-in of his ministers and parliamentary secretaries from 11am.
The roll call included 18 cabinet ministers, 11 ministers and 12 parliamentary secretaries.
Mr Abbott said he would govern for all Australians, including those who didn't vote for him.
"We won't forget those who are often marginalised, people with disabilities, indigenous people and women struggling to combine career and family," he said.
"We will do our best not to leave anyone behind."
Mr Abbott said it was an honour to serve the nation.
"We aim to be a calm, measured, steady and purposeful government that says what it means and does what it says," he said.
"We hope to be judged by what we have done."
Mr Abbott then introduced his team to subscribe the oath of office before the governor-general.
Deputy Prime Minister, Nationals leader and infrastructure and regional development minister Warren Truss led the way, followed by foreign minister Julie Bishop, employment minister Eric Abetz, Attorney-General George Brandis and Treasurer Joe Hockey.
The entire proceedings ran for almost two hours.
The new government will have at least 90 MPs in the 150-member House of Representatives, against the ALP's 55 and about five crossbench MPs.
Former Labor prime minister Kevin Rudd said on Twitter: "With Mr Abbott's swearing in today I cease formally to be Prime Minister.
Thank you Oz for the opportunity to serve. KRudd."
Mr Rudd and wife Therese Rein are "now off OS for a few weeks of R&R".
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