Colleagues from her cable news days said she was among the more serious reporters who appeared on Fox News’s morning lineup. “It’s no more unusual than a businessman ending up as president,” said Greta Van Susteren, a former Fox anchor. “She’s smart, she’s traveled the world, and she can talk to people, and that’s essentially what we need at the U.N.”

Ms. Nauert would not be the first television journalist to be sent to the United Nations. President Richard M. Nixon appointed John A. Scali, an ABC News correspondent, to be his special consultant for foreign affairs and communications in 1971 and then two years later made him ambassador to the United Nations.

At the time, there was criticism, but Mr. Scali had spent years covering foreign affairs and even played a crucial role as a secret intermediary between the United States and the Soviet Union during the Cuban Missile Crisis in 1962.

Ms. Nauert is one of numerous television personalities with roles in Mr. Trump’s as-seen-on-TV administration. Mr. Bolton was a Fox contributor, and Bill Shine, a former Fox co-president, serves as deputy chief of staff. Larry Kudlow, a longtime CNBC host, stars as the president’s chief economic adviser.

Ms. Nauert, 48, had to overcome a steep learning curve and a rocky relationship with her first boss, Rex W. Tillerson, the former secretary of state, who viewed her as a White House spy and did not take her on many trips. She repeatedly talked about quitting. But she developed a bond with Mr. Tillerson’s successor, Mr. Pompeo, who has promoted her within, and some former colleagues said she was a hard worker and quick study.

She is also a favorite of Ms. Trump and Mr. Kushner, who pushed for her selection. “Heather is smart, strong and strategic,” Ms. Trump said in a statement. “We are grateful for her continued service to our nation and administration.”

Critics were less generous, pointing to gaffes during her State Department tenure. On a trip to Saudi Arabia in October, Ms. Nauert posted on Instagram a smiling selfie outside a government complex in Riyadh, a discordant image given that the purpose of the visit was to discuss the brutal murder of the Saudi journalist Jamal Khashoggi.