Rex Tillerson set to be secretary of state

US President-elect Donald Trump has selected Exxon Mobil CEO Rex Tillerson to lead the State Department.

That's according to two people close to Trump's transition team.

The decision caps a lengthy process that often played out In public and exposed rifts within Trump's transition team. But Tillerson's close ties to Russia could still complicate his Senate confirmation hearings.

Trump was set to formally announce Tillerson's nomination on Tuesday morning (Wednesday AEDT). The people close to Trump's transition insisted on anonymity because they were not authorised to disclose the pick ahead of the announcement.

Trump's choice has already attracted criticism due to Tillerson's close ties with Moscow, where he represented Exxon's interests in the 1990s. In 2013 he was even awarded the Order of Friendship by the Russian government

Both Republican and Democratic politicians have warned Tillerson will be grilled in the Senate, which has to confirm his appointment.

Republican Senator John McCain said Tillerson's connections to President Vladimir Putin were 'a matter of concern to me.'

However the decision would fit with Trump's campaign promise of improving relations with Moscow.

In a message on his Facebook page late Monday, Romney indicated he had been rejected for the secretary of state job, saying his talks about the position with Trump had been 'enjoyable and enlightening.'

'I have very high hopes that the new administration will lead the nation to greater strength, prosperity and peace,' he said.

Australian Foreign Minister Julie Bishop said she looks forward to working closely with whomever Trump chooses.

'Rex Tillerson is known to us as the head of Exxon mobile and there are many Australians who have worked with him and he is well-known to us,' Ms Bishop told reporters in Canberra on Tuesday.

'I will deal with the realities of any changes in foreign policy position if and when they occur.

'Of course we are focusing on likely shifts in foreign policy but I think it would be more productive for me to make any comments once they were reality not a hypothetical,' she said.

Earlier on Monday, Trump named retired general John Kelly to lead the Homeland Security Department, and his transition team announced his intent to appoint Gary Cohn, president of the investment bank Goldman Sachs, to be one of his top economic advisers.

Both appointments had been expected.

If confirmed by the US Senate, Kelly will lead the Homeland Security Department's sprawling bureaucracy, created in the wake of the 2001 terrorist attacks.

The position includes disparate responsibilities involving security at airports, along US borders and disaster response.

Kelly was commander of the US Southern Command, whose roles include defending the US southern border and interagency co-operation against drug trafficking and human trafficking in Central and South America and the Caribbean.

Trump has vowed to halt illegal immigration, build a wall at the Mexican border and deport people who are in the US illegally.

Meantime, Trump says he will leave his businesses before his inauguration on January 20th.

'Even though I am not mandated by law to do so, I will be leaving my busineses (sic) before January 20th so that I can focus full time on the Presidency,' Trump tweeted.

'Two of my children, Don and Eric, plus executives, will manage them. No new deals will be done during my term(s) in office.'