A Florida lawmaker known for his tough stance toward China has been selected by President-elect Donald Trump as his next national security adviser, while another is tipped to be secretary of state.

Military veteran and Florida House member Michael Waltz was chosen by Trump as national security adviser – a key role that advises the president on the US response to foreign threats.

Meanwhile, Senator Marco Rubio is expected to be Trump’s future secretary of state, sources told the BBC’s US partner, CBS News. But the pick is not yet confirmed.

Trump confirmed Tuesday that he wanted South Dakota Governor Kristi Noem to play a significant role – as homeland security secretary.

Trump’s administration is starting to take shape after his win in last week’s presidential election.

Republicans also are closing in on full control of Congress. They have won back control of the Senate, the upper chamber, and are inching towards a majority in the House, the lower chamber, as vote-counting continues.

Some of the appointments – including secretary of state – will require senators’ approval, although Trump, also a Republican, has demanded that the next Senate leader let him bypass this. He can give out other jobs – like national security adviser – directly.

On Tuesday, Trump officially announced Waltz as the next national security adviser, praising the Florida congressman as an “expert on threats posed by China, Russia, Iran and global terrorism”.

Trump added that Waltz is a “strong champion of my America First Foreign Policy agenda”.

The appointment of Waltz and Noem, as well as possibly Rubio, come after Trump made Susie Wiles his chief of staff, named former immigration official Tom Homan as his “border tsar” and nominated New York Congresswoman Elise Stefanik as his future ambassador to the United Nations.

A president-elect is responsible for about 4,000 political appointments. During his first presidency, it took Trump months to assemble his cabinet.

It is not yet certain that Rubio, 53, will be nominated to serve as secretary of state – a role that functions as America’s top diplomat – but the Florida Republican’s career has set him up to take the role.

Several US media outlets have reported that Rubio is in talks with the Trump transition team over the senior position, but it has not been finalised. It appears the president-elect could still change his mind.

Rubio serves as the vice-chairman of the Senate Intelligence Committee and sits on the Foreign Relations Committee.

He is considered a foreign policy “hawk” – meaning someone who takes hard-line positions – towards Iran as well as China.

While supportive of Ukraine, he previously said the country’s war with Russia needed to “be brought to a conclusion”.

Rubio and Trump were opponents in the race for the Republican presidential nomination in 2016 and the two developed a bitter rivalry.

They clashed on a variety of issues – particularly immigration – and the conflict led to various insults. Trump referred to the senator as “little Marco” and Rubio mocked Trump’s “small hands”.

But Rubio went on to endorse his rival and campaigned for him ahead of the 2024 election. He was also in the frame to be Trump’s running mate – a role that ultimately went to JD Vance, who takes a similar view towards China.

Rubio, the son of working-class Cuban immigrants, was first elected to the Senate in 2010.

Waltz, 50, a military veteran and a long-time Trump supporter, was re-elected to Congress last week.

He was named national security adviser – which would involve identifying and countering threats to the US. The appointment would not require Senate approval.

Waltz is a decorated Green Beret and army veteran, having served multiple tours in Afghanistan, the Middle East and Africa.

In his book, Warrior Diplomat: A Green Beret’s Battles from Washington to Afghanistan, he documented his experiences serving in the Pentagon during the George W Bush administration and in combat operations overseas.

Like Rubio, Waltz has taken a tough line on China. As chair of the Armed Services Subcommittee on Readiness, he argued the US needed to do more to prepare for conflict in the Pacific.

He has also said the US should maintain its support for Ukraine, but in recent weeks has advocated for a reassessment of US spending on aid for the war effort.

Waltz has said Nato allies should increase their defence spending, though he has not gone as far as Trump – who has reportedly suggested the US could leave the Western military alliance, to which it is the main contributor.

“Look, we can be allies and friends and have tough conversations,” Waltz said last month.

Since the 2021 withdrawal from Afghanistan, Waltz has frequently criticised President Joe Biden and the White House.

He is the second member of Congress asked to serve in the next Trump administration, which would require him to resign his office in the House of Representatives.

That could have ramifications if the Republicans end up controlling the House with a slim majority. Waltz’s resignation would cut any majority by one until a replacement could be elected.

Waltz will be the fifth national security adviser to serve under Trump, who appointed four different men to serve in the position during his first term.

Trump sacked three of them: Michael Flynn, HR McMaster and John Bolton. The latter of the three actively campaigned against Trump in the 2024 election.

If confirmed, Noem, 52, would have a key role overseeing the security of the US – covering border, cyber threats, terrorism and emergency response.

The agency has a $62bn (£48bn) budget and employs thousands of people.

She would work closely with Homan and Stephen Miller, who is in charge of policy, to deliver Trump’s immigration pledges.

Noem was passed over to be Trump’s running mate in part over a bizarre admission that she killed her pet dog.

She dropped out of college at age 22 to run her family farm. Noem was elected as South Dakota’s first female governor in 2018.

Trump reportedly once told Noem he would like to have his face added to Mount Rushmore – the giant monument to past presidents carved into a mountainside in her home state.

Instead, she gave him a miniature replica – a 4ft (1.2m) bust showing his face alongside former presidents George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln.

North America correspondent Anthony Zurcher makes sense of the race for the White House in his twice-weekly US Election Unspun newsletter. Readers in the UK can sign up here. Those outside the UK can sign up here.