Haley, the first woman chosen for a senior job in Trump's administration, is "a proven dealmaker, and we look to be making plenty of deals. She will be a great leader representing us on the world stage," the Republican president-elect said in a statement.
A 44-year-old Republican and the daughter of Indian immigrants who is a voice for tolerance, Haley took Trump strongly to task during the presidential campaign over his harsh rhetoric about illegal immigration and for not speaking forcefully enough against white supremacists.
Trump has so far chosen five white men for senior positions as he shapes his administration following his victory over Democrat Hillary Clinton in the Nov. 8 election. Trump takes over from Democratic President Barack Obama on Jan. 20,
The choice of Haley may be aimed at countering criticism of Trump's divisive comments about immigrants and minorities, as well as accusations of sexism during his election campaign.
Haley led a successful effort last year to remove the Confederate battle flag from the grounds of the South Carolina state capitol after the killing of nine black churchgoers in Charleston. The flag was carried by pro-slavery Confederate forces during the U.S. Civil War and is viewed by many as a racist emblem.
Haley said she had accepted Trump's offer and would remain governor pending her confirmation to the Cabinet-level post by the U.S. Senate.
"When the president believes you have a major contribution to make to the welfare of our nation, and to our nation's standing in the world, that is a calling that is important to heed," she said in a statement.
As with Trump's future secretary of state, her job may include reassuring allies worried about some of Trump's campaign rhetoric, including his pledge to build a wall along the U.S.-Mexican border to curb illegal immigration, his promise to review trade agreements and his suggestion that he would push NATO partners to pay more for their own defense.
Trump wants a better relationship with Russia, a permanent member of the U.N. Security Council. He has antagonized China, another major power at the United Nations, with his rhetoric on trade and territorial disputes in the South China Sea.
Britain, a close ally in the U.N. Security Council, was upset that Prime Minister Theresa May was not among the first leaders that Trump spoke to after his election win.
Trump gave few clues about his world view during an extensive interview with The New York Times on Tuesday.
Asked what he sees as America's role in the world, Trump answered: "That's such a big question." When pressed more, he described the Iraq war as a mistake, urged better relations with Russia and called for an end to "that craziness that’s going on in Syria."
The United States is one of the five permanent veto-powers on the 15-member Security Council, along with Britain, France, China and Russia. It is also the largest funder of the United Nations, paying more than a quarter of the $8 billion peacekeeping budget and 22 percent of the several billion dollar regular budget.
The New York real estate magnate, who has never held public office, has made his team's deliberations for senior jobs a public affair, issuing a daily list of his meetings and announcing some impressions of potential candidates on Twitter.
He picked three conservatives to lead his national security and law enforcement teams last week, suggesting he plans to make good on his campaign promises to take a hard line on Islamist militancy and curbing illegal immigration
But a relative moderate, former Republican presidential nominee Mitt Romney, is under active consideration to head the State Department, along with other candidates.
Haley would succeed Obama's U.N. envoy, Samantha Power, a foreign policy expert before she took the job. In contrast, Haley, a state lawmaker before becoming governor, has little experience in international relations.
Trump transition team spokesman Jason Miller played up her foreign trade dealings as a governor.
“She’s done a fantastic job with the state of South Carolina, in helping to improve the economy. That included a number of overseas trade and business recruitment missions,” he said.
SHARP WORDS FOR TRUMP
Haley was a robust critic of Trump during the early stages of the primary race to pick the Republican presidential nominee, including condemning him for not disavowing the support of white supremacist group Ku Klux Klan and one of its former leaders, David Duke.
In a rebuttal to Obama's State of the Union address in January, Haley called for tolerance on immigration and civility in politics, in what some saw as a rebuke of Trump.
"During anxious times, it can be tempting to follow the siren call of the angriest voices," she said. "We must resist that temptation."
She supported Trump rivals Marco Rubio and Ted Cruz, both U.S. senators, in the Republican primary before saying last month she would vote for Trump despite reservations about his character.
Haley also criticized Trump last winter for not releasing his tax returns, prompting him to hit back on Twitter, "The people of South Carolina are embarrassed of Nikki Haley!"
Trump, who was in Florida for the Thanksgiving break, was expected to announce later on Wednesday that he has chosen Ben Carson to lead the U.S. Department of Housing and Urban Development.
"After serious discussions with the Trump transition team, I feel that I can make a significant contribution particularly to making our inner cities great for everyone," Carson, a former presidential candidate, wrote on Facebook.
"An announcement is forthcoming about my role in helping to make America great again," he added.