Trump has officially announced his appointment of Florida Rep. Mike Waltz as his national security adviser.

The president-elect highlighted Waltz's military background in a statement on the appointment, noting that he is the first Green Beret to have been elected to Congress and served in the Army Special Forces for 27 years.

"Mike has been a strong champion of my America First Foreign Policy agenda, and will be a tremendous champion of our pursuit of Peace through Strength!" Trump said in a statement.

The national security adviser is appointed by the president without confirmation by the Senate.

-ABC News' Soo Rin Kim, Kelsey Walsh and Lalee Ibssa

While control of the House has not yet been projected by ABC News, Republicans are inching toward maintaining their slim majority.

But already, Trump has picked several lawmakers to serve in his administration: Rep. Elise Stefanik for United Nations ambassador and Rep. Mike Waltz for national security adviser.

Speaker Mike Johnson, asked about the issue on Tuesday, said he's spoken to Trump about it several times.

"We have a really talented Republican Congress ... Many of them can serve in important positions in the new administration. But President Trump fully understands, appreciates the math here and it's just a numbers game," Johnson said. "You know, we believe we're going to have a larger majority than we had last time."

The speaker added: "I don't expect that we will have more members leaving, but I’ll leave that up to him."

Billionaire John Paulson said Tuesday he does not plan to formally join the administration as the secretary of the U.S. Department of the Treasury, though he said he intends to remain actively involved with Trump's economic team.

"Although various media outlets have mentioned me as a candidate for Secretary of the Treasury, my complex financial obligations would prevent me from holding an official position in President Trump’s administration at this time," Paulson said in a statement.

"However, I intend to remain actively involved with the President’s economic team and helping in the implementation of President Trump’s outstanding policy proposals," he added.

-ABC News' Beatrice Peterson

House Speaker Mike Johnson confirmed that Trump is expected to visit the U.S. Capitol to celebrate a potential Republicans "trifecta" on Wednesday morning before he sits down in the Oval Office with President Joe Biden later in the day.

"Well, I'll say I didn't intend to break this as news this morning," Johnson quipped as he held a press conference with House Republican leadership.

"He wanted to come and visit with House Republicans, so we're working out the details of him gathering with us potentially tomorrow morning, before he goes to the White House," Johnson said. "And that would be a great meeting and a moment for all of us, there's a lot of excitement, a lot of energy here. We're really grateful for President Trump leaving it all on the field to get reelected."

ABC News' John Parkinson, Isabella Murray and Lauren Peller