He was the first of 42 government executives to be sworn in by Governor General Quentin Bryce at a ceremony at Government House in the capital Canberra yesterday.
He has been criticised for including only one woman in his 19-member Cabinet, Foreign Minister Julie Bishop - although she will be Australia's first woman named to that post.
His conservative party defeated former prime minister Kevin Rudd's center-left Labour Party in the September 7 elections.
Mr Abbott announced Australia's controversial new policy on asylum seekers that includes turning back their boats to Indonesia would begin immediately after the swearing in ceremony.
Australia has seen an increase in the number of such asylum seekers from Iran, Afghanistan, Pakistan, Vietnam and other countries.