"You obviously enjoyed hearing it, so let me say it again: The government of Australia has changed," Abbott told jubilant supporters at the Four Seasons Hotel in Sydney.
55-year-old Abbott, a former boxer, Rhodes scholar and trainee priest, promised to restore political stability, cut taxes and crack down on asylum seekers arriving by boat.
It was the frustration with Labor's leadership turmoil that cost the government dearly at the polls.
Labor dumped Prime Minister Kevin Rudd in 2010 for Australia's first female prime minister Julia Gillard, only to reinstate Rudd as leader in June 2013 in a desperate bid to stay in power.
As Abbott and his family enjoyed rapturous applause, an interloper managed to make his way onto the stage before being spotted and forcibly removed.