Former Australian Prime Minister Malcolm Turnbull speaks during his final press conference before leaving Parliament in Canberra. Picture: Andrew Taylor/AP

Canberra - Former Australian prime minister Malcolm Turnbull, who was ousted from the post in a brutal conservative rebellion last week, has resigned from parliament.

Turnbull, the country's 29th prime minister, who first entered parliament in 2004, handed his resignation letter to the speaker of the lower house, Tony Smith, on Friday.

His resignation will trigger a by-election in his Sydney electorate of Wentworth, which could threaten the coalition government's one-seat majority in the lower house of parliament.

Turnbull was ousted as Liberal party leader, and thus as prime minister, one week ago following a rebellion led by one of his senior ministers and a week of rumours, threats and backstabbing.

Turnbull lost the support of his colleagues largely due to poor results in July by-elections and disagreement over his climate and energy policies.

Australians have had seven prime ministers in 11 years. A series of internal leadership coups has meant that no prime minister has served an entire term in office since 2007.

Earlier this week, Turnbull said the best place for a former prime minister was out of parliament.  

"I don't want to dwell on recent shocking and shameful events - a malevolent and pointless week of madness that disgraced our Parliament and appalled our nation," he said on Wednesday in a letter addressed to his electorate.

He also highlighted some of the major achievements of his government, including the legalization of same-sex marriage, the establishment of a national redress scheme for victims of child sex abuse, and strong economic and job growth. 

Turnbull was replaced by his treasurer, Scott Morrison, who was not part of the rebellion, after winning the party leadership contest in an internal ballot.

Morrison, who is on an official visit to Indonesia, paid tribute to Turnbull on Friday as a prime minister who "delivered some very big things for Australia."

"Malcolm has been a dear and close friend to me for a very long period of time and he has served his country well and grandly," Morrison told reporters in Jakarta.

Both Morrison and Turnbull are from Sydney. 

To Turnbull's retirement, Morrison said: "You deserve that mate, you absolutely deserve that. You've served our country well, and on behalf of our country as prime minister, I just want to say thanks."

Turnbull will fly out to New York for a six-week holiday this weekend, local media reported.

The date for the by-election has not been announced, but it is expected to be in October.

The harbour-side electorate is a plum seat for the conservative Liberal party, as Turnbull has held it for 14 years.

Opinion polls have already shown huge voter backlash for the Liberals due to the infighting. The party will have to field someone similar to Turnbull, who is considered to be a more moderate figure inside the party.

A number of potential candidates have already put their hands up for the Liberal pre-selection, including Christine Forster, the sister of former prime minister Tony Abbott, who was one of the co-plotters of Turnbull's demise.