Mr Abbott issued a short statement on Sunday night saying he would contest the seat of Warringah.
He has held the seat on Sydney's northern beaches for 22 years.
Malcolm Turnbull replaced Mr Abbott as prime minister after winning a ballot for leadership of the ruling Liberal Party in September.
Mr Abbott said he had taken time out to assess his future since losing the leadership and was heartened by the support that he had received from his constituents.
"Therefore, I am renominating to represent the people of Warringah for another term as their Liberal MP," he said.
Mr Abbott's decision to stay in politics immediately drew comparisons to Kevin Rudd, the Labor prime minister who was dumped by his own party in 2010.
Mr Rudd's desire to return to the leadership was seen as a destabilising force for the Labor government and the prime minister who replaced him, Julia Gillard.
Mr Rudd eventually won back the leadership from Ms Gillard, but led Labor to defeat against Mr Abbott in the 2013 federal election.
Liberal senator and Abbott loyalist Eric Abetz dismissed the comparisons, telling the Australian Broadcasting Corp. that Mr Abbott was "no Kevin Rudd".
"Kevin Rudd was always about one thing only, Kevin Rudd, whereas Tony Abbott has always been about one thing, namely, the Australian people," Mr Abetz said.
Deposed Australian prime minister Tony Abbott will attempt to stay in parliament at the country's next federal election.