Prime Minister-designate Malcolm Turnbull says he will lead a "thoroughly Liberal government" and has paid tribute to his predecessor, Tony Abbott, after winning a late-night ballot for the Liberal Party leadership.

The former communications minister defeated Mr Abbott 54 votes to 44 in a party room ballot which also saw Julie Bishop re-elected as deputy leader ahead of Kevin Andrews 70 votes to 30.

The new leadership team fronted the media just after 10:40pm (AEST) where Mr Turnbull said he was humbled by the honour bestowed on him.

"This has been a very important, sobering experience today. I'm very humbled by it," he said.

The Prime Minister-designate paid tribute to Mr Abbott, who delivered the Coalition victory at the 2013 election.

"I want to say at the outset what a great debt the nation owes and the party owes, the Government owes to Tony Abbott and of course, to his family Margie and their daughters," Mr Turnbull said.

"The burden of leadership is a very heavy one. Tony has discharged that as leader of the party and, of course, as prime minister over many years now and the achievements of the Government that he has led have been formidable."

Mr Turnbull said he would lead a "thoroughly Liberal government" committed to freedom, the individual and the market.

"We need to have in this country, and we will have now, an economic vision, a leadership that explains the great challenges and opportunities that we face, that describes the way in which we can handle those challenges, seize those opportunities, and does so in a manner that the Australian people understand so that we are seeking to persuade rather than seeking to lecture."

He added: "The Australia of the future has to be a nation that is agile, that is innovative, that is creative. We can't be defensive, we can't futureproof ourselves.

"We have to recognise that the disruption that we see driven by technology, the volatility in change is our friend if we are agile and smart enough to take advantage of it."

Mr Turnbull hosed down speculation that he would call a snap election and said "his assumption" was that the Parliament would serve its full term.

"Inevitably there will be changes in ministerial arrangements. I'll be meeting with the ministry [Tuesday] morning," he said.

"I expect ministers will continue in their current position unless, of course, they choose not to for the balance of the week and we'll make ministerial changes after the parliamentary sitting week is over."

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Parliamentary secretary Steve Ciobo said Scott Morrison was anticipated to become treasurer, replacing Joe Hockey who was critical of Mr Turnbull after the leadership spill was called.

There have also been reports that key South Australian MP Christopher Pyne would be handed the defence portfolio and deliver multi-billion-dollar submarine projects for the state.

Mr Turnbull said the challenge for any leader would be to bring together the broad church of the Liberal Party.

"The partnership with our colleagues will be a very clear cultural demonstration that we are operating in a traditional Cabinet manner and that means that I'm not going to make policy pronouncements from this podium tonight.

"Of course policies change, they change all the time, but they will be when people should have the confidence that we will be making decisions in a thoughtful and considered manner, recognising the significance of the work we have to do as the Government of Australia."

Nationals warn against recriminations

Ms Bishop said she was excited to be continuing to serve as deputy leader under Mr Turnbull.

"I came into the Liberal Party and came into Parliament because I believed in the values of the Liberal Party, because I believe that they provide the most hope for the most people in this country ," she said.

"And as a believer in the Liberal Party that was created by Robert Menzies, I am furthermore of the view that the values and beliefs of the Liberal Party are as relevant today as they were when this great party was formed seven years ago.

"In Malcolm Turnbull, we have a leader who will be true to those Menzian values and beliefs and I'll be honoured to serve this party and this country in my current role."

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But senator Cory Bernardi, a staunch supporter of Mr Abbott, said politics in Australia was becoming a "circus".

"We have now probably had so many prime ministers and leaders of oppositions in the last eight years that I think we've set a new record for the entire Pacific," he said.

"Is that really a badge of honour that we want? I'd suggest no, and the people that have been rewarded today have been instrumental in that instability and I feel for the PM Tony Abbott."

Deputy Nationals leader Barnaby Joyce warned against recriminations within the Coalition.

"A Coalition agreement is an agreement between the leaders of the party, between the leader of the National Party Warren Truss and the leader of the Liberal Party who at the time was Tony Abbott," he said.

"We must make sure that we have a leader that can lead a Coalition, not just a leader that can lead the Liberal Party.

"So for that purpose, we need to make sure that the views that are well held by the National Party, who obviously didn't get a chance to vote in that vote tonight, are understood and incorporated in any government going forward."

He said Mr Turnbull needed to strike a new deal with its junior Coalition partner.

"There is no Liberal Party government, there is only a Coalition government. Without a Coalition government you don't have a government," Mr Joyce said.

'It will always be about Malcolm'

After the vote, Opposition Leader Bill Shorten tweeted: "Australians know that with Malcolm, it will always be about Malcolm.

"Australia doesn't need another Liberal Leader — we need a change of government, and Labor's up for the fight."

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Opinion polls had consistently shown voters preferred Mr Turnbull to lead the Liberal Party.

Throughout his career — as a lawyer, investment banker and then politician — he set out to be noticed.

As a minister in the Howard and Abbott governments, he has been known for his intellect and strong communication skills.

Mr Turnbull held the top job in Opposition but lost a ballot in 2009 to Mr Abbott by one vote. He was ultimately brought down over his support for an emissions trading scheme.

Some of his colleagues are wary of his return for his stance on climate change policy and support of same-sex marriage. Others believe he is their best chance of a revival.

As communications minister, he has reinvented the National Broadband Network but has also been pivotal in serious internal debates on counter-terror laws.

At one year, 361 days, Mr Abbott — who faced what he called a "near-death experience" in February when MPs gave him six months to turn around the Government's fortunes — served the shortest time as prime minister since Harold Holt.