Mr Abbott, 55, took the oath at Government House in Canberra in front of Governor-General Quentin Bryce.
His conservative coalition won a comfortable lower house majority in the 7 September polls, BBC reported.
It plans to scrap a tax on carbon emissions introduced by Labor and further toughen asylum policy.
Ahead of Wednesday's ceremony, Mr Abbott said his government would get to work immediately.
"Today is not just a ceremonial day, it's an action day," he said. "The Australian people expect us to get straight down to business and that's exactly what this government will do."
The new ministers were also being sworn in during the day. His 19-member cabinet line-up has caused debate because it contains only one woman, new Foreign Minister Julie Bishop.
Mr Abbott, however, says his cabinet is "one of the most experienced incoming ministries in our history".