Malcolm Turnbull has used his first appearance at Question Time as the 29th Prime Minister of Australia to acknowledge and thank Tony Abbott for his work during almost two years in power.

Mr Turnbull said the Coalition owed Mr Abbott "an enormous debt of gratitude for his leadership and service" over many years.

"He led us out of opposition, back into government," Mr Turnbull said.

"The challenges of leadership are very considerable, the pressures are enormous, and as Tony Abbott has often said himself, very, very profoundly, that all of us here are volunteers, it is our families that are conscripts."

Mr Turnbull said the government and the opposition should also acknowledge the debt by Mr Abbott's wife Margie, and their daughters.

"Tony has discharged his role as prime minister, indeed as leader of the opposition, with enormous distinction and achievement," Mr Turnbull said, as members of the opposition heckled.

"The Free Trade Agreements alone, which have been negotiated under his leadership, represent some of the most significant foundations for our future prosperity.

"Under his leadership, our government restored the integrity of our borders ... Mr Speaker, we owe a great debt to Tony Abbott, we thank him for his leadership, we thank him for his service, he is a great Australian, and our country has been better, has been improved, has been better lead under his time as prime minister."

Mr Turnbull is expected to reshuffle his Cabinet over the weekend.

Senior Abbott supporters - including Treasurer Joe Hockey, Senate leader Eric Abetz and Defence Minister Kevin Andrews - will likely be moved on.

More women are expected to be promoted in the reshuffle, with Marise Payne, Michaelia Cash and Kelly O'Dwyer among those eyeing higher honours.

Opposition Leader Bill Shorten also addressed Question Time to address his own fond memories of Tony Abbott during his time as Prime Minister.

"It is part of the Australian spirit not to score points when someone is down," he said.

"So I just want to say, that public life is hard on people who serve and it's hard on their families.

"It is not for me to be partisan about Mr Abbott's record, but he certainly had led the Liberal party formidably for well in excess of five years."

Mr Shorten said Mr Abbott was a "fierce proponent of his views" and a "ruthless advocate for what he believes in".

"I have exchanged harsh words with him in my time as opposition leader, I've disagreed with his politics and decisions on many occasions," he said.

"But I also wish to record that he also had this frustrating ability on occasion just when you were really frustrated with a particular decision he might have made, to do something unexpected and generous and personal."

Mr Shorten referred to the death of his mother, and how Mr Abbott had made a "sensitive" gesture.

Turnbull's swearing in ceremony as Prime Minister was brief. (9NEWS)

Less than an hour earlier, Mr Turnbull had been sworn in as prime minister at a ceremony at Government House in Canberra, following last night's leadership spill that resulted in Tony Abbott's resignation.

Governor General Peter Cosgrove led the brief ceremony before he, wife Lynne, Mr Turnbull and his wife Lucy posed for official photos outside.

Deputy Leader Julie Bishop joined the group a short time later, as did Mr Turnbull's family.

Earlier today, Mr Turnbull arrived at Parliament House for the Liberal party room meeting alongside Ms Bishop, who was re-elected as deputy leader, and their Liberal party colleagues.

Has the change in leadership made you more or less likely to vote Liberal? More likely 22100 Less likely 17484

Upon leaving his Canberra apartment this morning, Mr Turnbull told reporters he was filled with optimism.

"There has been a change of prime minster but we are a very, very strong government," he said.

When asked if it was a dream come true, Mr Turnbull said he did not expect yesterday's turn of events.

"But it's one that I'm privileged to undertake and one that I'm certainly up to," he said.

READ MORE: Tony Abbott addresses the nation for the final time as Prime Minister

Earlier today, Mr Abbott offered his final address to the nation as Prime Minister, and said he was proud of his government's achievements.

"It is humbling to lose, but that does not compare to the honour of being asked to lead," he said.

"I have consistently said in opposition and in government that being the prime minister is not an end in itself - it's about the people you serve."

Do you think Tony Abbott did a good job as prime minister? Yes 11683 No 12944

Among his government's achievements he listed the creation of 300,000 jobs, abolished taxes, free trade agreements, infrastructure, the royal commission into union corruption and responding to threats of terror.

He said in stopping the boats, the government had been better able to display compassion to refugees.

He acknowledged there was more he would have liked to do, including constitutional recognition of Indigenous Australians, and addressing the challenges of ice and domestic violence.

After a tense 30-minute wait last night, Chief Government Whip Scott Buchholz emerged from the meeting to announce Mr Turnbull had won the vote 54-44.

Do you think Julie Bishop made the right decision? Yes 12023 No 7623

Ms Bishop was re-elected as deputy Liberal leader, defeating Kevin Andrews 70 votes to 30.

"Tonight there were two ballots conducted; one ballot for leader, one ballot for deputy leader," Mr Buchholz said.

"Malcolm Turnbull was successful on 54, Tony Abbott on 44 and one was informal."

The meeting was called after Mr Turnbull approached Mr Abbott after question time yesterday afternoon to request a leadership ballot.

Mr Turnbull used his first speech after being elected leader to thank Mr Abbott for his time as prime minister.

"This has been a very important day in the life of the nation, the government and of course of our party," Mr Turnbull said.

"I want to say at the outset, what a great debt the nation owes, the government owes, the party owes to Tony Abbott, and of course to Margie and their daughters.

"The burden of leadership is a very heavy one.

"Tony has discharged that over many years now. The achievements of the government he has led have been formidable."

The prime minister-elect vowed to offer a new style of communication with the public and improved economic leadership.

"This has been a very important, sobering experience today," Mr Turnbull told reporters.

"I’m very humbled by it.

"I’m very humbled by the great honour and responsibility given to me today.

"We need to have in this country – and we will have now – the economic vision and a leadership which explains the economic challenges which we face."

Mr Turnbull did not outline any major policy changes in his speech but outlined his vision for his government and the nation in years to come in an impassioned message to the public.

"This will be a thoroughly liberal government," he said.

"It will be thoroughly liberal government committed to freedom, the individual and the market.

"The Australia of the future has to be a nation that is agile, that is innovative, that is creative.

"There has never been a more exciting to be alive than today, and there has never been a more exciting time to be in Australia."

Mr Turnbull was elected to the Sydney eastern suburbs seat of Wentworth in 2004 after a decorated business and legal career.

Do you think Australia's political instability is embarrassing? Yes 17386 No 3153

He was elected as Liberal leader while in opposition in September 2008 but was ousted by Mr Abbott in December 2009.

Mr Abbott served as prime minister for almost two years, losing the leadership just four days shy of marking his second anniversary in office.

Are you glad that Malcolm Turnbull has won the leadership of the Liberal party? Yes 20110 No 12133