Nauert joined the State Department in April 2017.
Trump describes Nauert to reporters as "very talented" and "very smart".
In October, Haley announced that she was leaving the post by the end of the year. Nauert was mostly a polished and unflappable defender of administration policy, smoothing over frequent rifts between the Trump's first secretary of state, Rex Tillerson, and the White House.
Heritage Foundation fellow Brett Schaefer said Nauert has proven she has the ability to explain and defend USA foreign policy, the core requirement for being a us ambassador to the world body.
Mr Trump earlier said his daughter, Ivanka, would be ideal for the role but conceded he'd be accused of nepotism if he appointed her.
A tough stance on North Korea remains one of the top agenda items for both the UN Ambassador and the Secretary of State.
To take over the Cabinet role, Nauert will need to be confirmed by the Senate.
A White House official says the Trump administration is downgrading the US diplomatic post at the United Nations to a non-Cabinet position.
Nauret posted a cutesy tourist picture form the country, which was criticized as inappropriate given the reason for her visit was to investigate the murder of an American resident. She hadn't specialized in foreign policy or global relations.
A key question with Nauert, 48, will be whether the president keeps the United Nations envoy job as a cabinet-level position, or downgrades it to report through Pompeo, as other administrations have sometimes done. If her much more recent experience at the State Department provides such rich fodder for critics, it portends a hard confirmation process ahead.
Schaefer notes, though, that Trump already has a team in place that he relies on for help in crafting foreign policy -Pompeo and National Security Adviser John Bolton. Before joining the State Department, Nauert did not have any previous government or diplomatic experience.
Trump's announcement comes just a day after the US lost a high-profile vote in the U.N. General Assembly for a resolution condemning the Palestinian militant group Hamas. With Mike Pompeo in charge of State, Nauert has been on the road much more.
"And one of his favourite shows is the popular morning show, Fox and Friends, and Nauert was associated with this show for several years, and that surely had something to do with her selection".
Ahead of the vote, the U.S. ambassador sent a letter to all UN missions to make clear that "the United States takes the outcome of this vote very seriously".