US media reports say President-elect Donald Trump has begun the process of choosing a cabinet and selecting other high-ranking administration officials following his presidential election victory.

Reuters reports that Mr. Trump said yesterday the he has picked as his Secretary of Defense Pete Hegseth, “a Fox News commentator and veteran who has expressed disdain for the so-called "woke" policies of Pentagon leaders including its top military officer”.

If confirmed by the U.S. Senate, Hegseth could make good on Trump's campaign promises to rid the U.S. military of generals who he accuses of pursuing progressive policies on diversity in the ranks that conservatives have rallied against, according to Reuters.

Mr. Trump yesterday also named Elon Musk and former Republican presidential candidate Vivek Ramaswamy to lead a newly created Department of Government Efficiency, rewarding two of his well-known supporters from the private sector.

Ramaswamy and Musk; photo / AFP

Musk and Ramaswamy "will pave the way for my Administration to dismantle Government Bureaucracy, slash excess regulations, cut wasteful expenditures, and restructure Federal Agencies," Trump said in a statement, according to Reuters.

The Guardian reports that despite the name, the Department will not be a government agency. Trump said in a statement that Musk and Ramaswamy will work from outside government to offer the White House “advice and guidance” and will partner with the Office of Management and Budget to “drive large scale structural reform, and create an entrepreneurial approach to government never seen before.” He added that the move would shock government systems, The Guardian noted.