Trump has said he wants the authority to fire civil servants he views as disloyal.
His opponents fear he will turn the Justice Department and other federal law enforcement agencies into political weapons to investigate perceived enemies.
Trump and his incoming vice-president, US Senator JD Vance, are set to take office on Inauguration Day, January 20.
He promised roles in his administration to Tesla chief executive Elon Musk, the world’s richest man, and former presidential candidate Robert F. Kennedy Jr.
The outcome defied polls that showed a razor-close race ahead of Tuesday’s Election Day.
Trump mopped up at least five so-called battleground states to push him over the 270 Electoral College votes needed to win the presidency.
He appeared headed for victory in the two remaining battleground states – Arizona and Nevada – where votes were still being tallied.
Trump’s lead over Harris stood at five million votes late on Wednesday, putting him on track to become the first Republican presidential candidate to win the popular vote since George W. Bush two decades ago.
His fellow Republicans won control of the US Senate from Democrats and stood a chance of adding to their narrow majority in the US House of Representatives, though the outcome there likely will not be known for several days.
“It was a hell of a good day,” said Mitch McConnell, the longtime Senate Republican leader.
Republican unity on Capitol Hill would clear the way for major portions of Trump’s legislative agenda, as it did in the first two years of his 2017-2021 presidency when Republicans whipped a major tax-cut Bill through Congress that mainly benefitted the wealthy.
“America has given us an unprecedented and powerful mandate,” Trump said early on Wednesday (US time) to a roaring crowd at the Palm Beach County Convention Center in Florida.
Harris, the US vice-president, called Trump to congratulate him, aides said, and they discussed the importance of a peaceful transfer of power and being a President for all Americans.
She will publicly concede the election to Trump later on Wednesday, a source told Reuters.
Major stock markets around the world rallied following Trump’s victory, and the dollar was set for its biggest one-day jump since 2020.
Trump was elected despite persistently low approval ratings, four criminal indictments and a civil judgment against him for sexual abuse and defamation.
In May, Trump became the first US president to be convicted of a crime when a New York jury found him guilty on 34 felony counts of falsifying business records to cover up hush money paid to a porn star.
Trump’s political career appeared to be over after his false claims of election fraud led a mob of supporters to storm the US Capitol on January 6, 2021, in a failed bid to overturn his 2020 defeat. Federal prosecutors indicted him although that and other criminal cases brought against him will now be shelved.
But he swept away challengers inside the Republican Party and then beat Harris by capitalising on voter concerns about high prices and what Trump claimed, without evidence, was a rise in crime because of illegal immigration.
Trump’s win will have major implications for US trade and climate change policies, Americans’ taxes and immigration, and US foreign policy, including in the Middle East and Ukraine.
Israeli Prime Minister Benjamin Netanyahu congratulated Trump, Netanyahu’s office said. They discussed “the Iranian threat” and the need to work together for Israel’s security, it said.
Hamas, the Palestinian militant group, called for an end to the “blind support” for Israel from the United States.
Ukrainian President Volodymyr Zelenskyy welcomed Trump’s commitment to “peace through strength,” while the Kremlin said it would wait and see if his victory could help end the war in Ukraine more quickly. Trump had said he could end the war in 24 hours but did not say how.
Heading into the election, voters identified jobs and the economy as the nation’s most pressing problem, according to Reuters/Ipsos opinion polls.
Many Americans remained frustrated by higher prices even amid record-high stock markets, fast-growing wages and low unemployment.