Nauert, 48, had been touted for the post since October when Haley announced that she was stepping down.
Trump also told reporters at the White House that he would make another staffing announcement on Saturday involving the Joint Chiefs of Staff, but gave no other details. She has been chief spokeswoman for the State Department since April a year ago, having been poached from Fox.
To take over the Cabinet role, Nauert will need to be confirmed by the Senate.
Asked whether the US was ever truly poised to attack North Korea, Haley told The Atlantic: "No".
During Pompeo's tenure, she has been able to travel on official trips - something Tillerson blocked her from doing - and rose to temporarily hold the position of acting under secretary for public diplomacy and public affairs.
In announcing his decision today, Trump said Nauert was "very talented, very smart, very quick". She was an anchor for Fox and Friends, the Fox News Channel morning program that Trump says he watches regularly. However, she quickly learned key issues and how the United Nations operates.
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Previously, she was a Fox News presenter and correspondent.
Nonetheless, during her two-year stint, Haley became a darling of the Trump administration and the pro-Israel community for her vociferous defense of the Jewish state at the United Nations, a body often seen as hostile to Israel.
Nauert has laid relatively low in the administration. She called the job an honor of a lifetime and said she wants to let someone else take it.
"If I were the State Department's spokesperson, on an official trip to learn more about the dark, dubious circumstances surrounding the disappearance of a U.S. resident, I probably would have skipped the tourist-in-Riyadh photos".
President Trump has picked Heather Nauert, the State Department's spokeswoman, as the next ambassador to the United Nations.
In her first interview since resigning as the US representative at the U.N. in October, Haley addressed the heated war of words between the two nations in the summer and fall of 2017. And the pick for the high-profile USA policy megaphone, seems more than justified, at least at first glance.
Nauert had little foreign policy experience before taking the podium as spokeswoman for the State Department.
The Illinois native would follow in the footsteps of Haley, a former governor of South Carolina; Samantha Power, a Pulitzer Prize victor; Susan Rice, a Rhodes Scholar; and former National Security Council and national security officials such as Madeleine Albright. Then-Senate Armed Services Chairman John McCain, R-Ariz., and others like Lindsey Graham, R-S.C. - now a close Trump ally - hammered Obama for giving a deputy national security adviser job to Ben Rhodes despite his lack of previous experience in those areas. "Ambassador Haley was a far more high-level figure, particularly early in the administration".