Donald Trump will head to the White House on Thursday to discuss with Barack Obama the transition of power.
It comes after Mr Trump was elected the 45th president by defeating Hillary Clinton in one of the most divisive elections in modern US history.
Speaking to reporters, Democrat Mr Obama admitted he and Republican Mr Trump have some “pretty significant differences” but “the presidency is bigger than any of us” as he vowed to ensure the transition was smooth and successful.
Mr Obama added: “We are rooting for his success in uniting and leading the country”, as he called on Americans on both sides of the political divide to remember “we are actually all on one team”.
Anti-establishment outsider Mr Trump, who has never held political office, stunned the world and upset the status quo with his unexpected victory.
The sitting President telephoned his successor to congratulate him on his win and also called Mrs Clinton to express his “admiration for the strong campaign she waged throughout the country”.
A triumphant Mr Trump walked on stage earlier to deliver his victory speech in New York to chants of “USA, USA!”
Wins in swing states such as Florida and North Carolina took him beyond the 270 Electoral College votes required to take the White House.
The celebrity businessman pledged to bind the wounds of division and called on Republicans and Democrats to come together after a “nasty” presidential race.
Mr Trump paid tribute to his rival for a hard-fought campaign and promised to be “president to all Americans”.
“The forgotten men and women of our country will be forgotten no longer,” he said. “I promise you I will not let you down.”
Mr Trump will not be inaugurated until 20 January – but thoughts are already turning to how his presidency will unfold after his at-times inflammatory rhetoric, as well as promises to build a wall at the Mexican border and to ban Muslims from entering the US.
There were anti-Trump protests on both US coasts from Pennsylvania to California, Oregon and Washington as hundreds of people marched through streets, with an effigy of the President-elect reportedly set on fire in Oakland.
In a message to the world, Mr Trump said “while we will always put American interests first… we will get along with all other nations… willing to get along with us.”
Mrs Clinton’s supporters were left stony-faced and in tears at what was supposed to be her victory rally, a short distance away in New York, before being sent home by her campaign manager.
Mrs Clinton later urged her supporters to accept the election resultand give Mr Trump the “chance to lead”.
Early exit polls had provided the Democrats with optimism, but shortly after 2am UK time the momentum began to shift as it emerged Mr Trump was edging ahead in a number of key states.
The first swing state to be called for Mr Trump was Ohio at around 3.30am, before others followed and Pennsylvania clinched it for the billionaire Republican just after 8am.
Exit polls also showed he triumphed by winning the backing of white, working class voters, particularly non-college-educated men, trumping Mrs Clinton’s coalition of mainly women, minorities and young people.
However, Mr Trump increased the Republican share of Hispanic voters – 29% versus Mitt Romney’s 27% in 2012.
Mrs Clinton looks set to win the popular vote across the country – but it is Electoral College votes that count.
World markets responded as the US map turned Republican red, with falls reported across Asia and the Mexican peso dropping to a record low against the dollar, while the FTSE 100 saw £37bn wiped off the value of top UK-listed companies but the index later recovered.
Canada’s main immigration website crashed and New Zealand reported an increase in traffic to its website for residency visas.
Cuba announced five days of pre-scheduled military exercises to prepare for what it called potential “enemy actions” following the election of Mr Trump.
Russian President Vladimir Putin was the first world leader to congratulate Mr Trump, saying he hoped for the two nations to engage in “constructive dialogue” on international issues.
British Prime Minister Theresa May said the UK’s “special relationship” with the US remained “strong and close”.
Acting UKIP leader Nigel Farage, who campaigned for Brexit in the UK and endorsed Mr Trump’s candidacy, is expecting to meet Mr Trump on Saturday in New York, according to Sky sources.
The 70-year-old will be the oldest person ever inaugurated as US President.
On what turned out to be a dream night for the Republicans, the party also retained control of the Senate and the House of Representatives.