"She's very talented, very smart, very quick, and I think she's going to be respected by all".
Nauert would need to be confirmed by the US Senate, but if she passes that hurdle, she would become a top voice for Trump's foreign policy.
Nikki Haley announced in October that she would step down at the end of this year
Some White House advisers were urging the president to consider another choice, believing that Ms. Nauert's lack of diplomatic experience would make Senate confirmation hard.
Trump's announcement comes just a day after the USA lost a high-profile vote in the U.N. General Assembly for a resolution condemning the Palestinian militant group Hamas.
Israeli leaders nonetheless thanked her and feted the results as proof of wide support for Israel's position.
"Nauert is a very good public operator, and should do a professional job presenting USA policy at the UN", Richard Gowan, a senior fellow at the United Nations University's Center for Policy Research, said in the Bloomberg report.
He said U.S. influence is at a "low ebb", partly because of the absence of empowered ambassadors under Trump.
European Union should worry about Huawei, other Chinese firms, says official
He also outlined the Byzantine structure and what he called a constantly changing nature of USA sanctions against Iran. Huawei is the world's biggest producer of telecoms equipment, operating in more than 170 countries and regions.
It was not immediately clear if Nauert would be able to defend Israel in the same powerful way as Haley did.
There is some relief at the United Nations that Trump did not pick another name on his short list of candidates: Richard Grenell, the USA ambassador to Germany, is a close ally of Bolton's, having served as U.S. spokesman at the United Nations while Bolton was ambassador there.
She was later appointed as acting undersecretary of state for public diplomacy and public affairs, making the former Fox News broadcast journalist one of the highest ranking women in the agency.
Mr Trump told reporters last month that Ms Nauert was "excellent", adding, "She's been a supporter for a long time".
The State Department used to hold daily briefings. Haley had lobbied hard to get the resolution passed, but couldn't garner the two-thirds majority needed.
Trump is leading US trade negotiations with China: Mnuchin
In his tweets , the president said his advisors will work on "seeing whether or not a REAL deal with China is actually possible". One Chinese official said officials were "waiting for the leaders to return" before publicising details.
Overnight she took charge of overseeing communication from USA diplomatic missions around the world as well as countering propaganda from the Islamic State movement and other foreign adversaries.
Before joining the administration in 2017, Nauert was a TV anchor for Fox News and won an Emmy nomination while working at ABC News. She is a graduate of Columbia University's Graduate School of Journalism and Mount Vernon College in Washington. Aides on the Senate Foreign Relations and Judiciary committees - which would take up the ambassador and attorney general nominations, respectively - said Friday that neither committee will hold confirmation hearings this year, given the limited time left before a new Senate takes over on January 3.
Meanwhile, the Indian permanent mission to the United Nations, which has developed a good relationship with Haley, is also likely to closely watch Nauert.
L’Aquarius bloqué à quai, SOS Méditerranée cherche un nouveau navire humanitaire
Depuis le début de ses opérations, l'Aquarius a porté assistance à près de 30.000 personnes. La semaine dernière Berne lui avait refusé le pavillon suisse.