Also on Tuesday, Trump confirmed that he wanted South Dakota Governor Kristi Noem to play a significant role as homeland security secretary. Another military veteran, Michael Waltz, was chosen by Trump as national security adviser – meaning he will advise the president on foreign threats.
Senator Marco Rubio – who shares Waltz’s hawkish views on China – is expected to be Trump’s future secretary of state, sources have told the BBC’s US partner, CBS News. But the pick is not yet confirmed.
Republicans have won back control of the Senate, the upper chamber of Congress, and are inching towards a majority in the House, the lower chamber, as vote-counting continues.
Some of the government appointments – including Hegseth’s – require a vote of approval by senators, although Trump, also a Republican, has demanded that the next leader of the US Senate let him bypass this process. He can give out other jobs directly.
Senate Republicans are due to vote on a new leader on Wednesday – the day that Trump is also expected to visit the outgoing president, Joe Biden, at the White House as part of the traditional transfer of power.