It appears that the two men spoke shortly before 4am on Wednesday

Trump campaign manager Kellyanne Conway described the conversation between the two men as 'very warm'

He also invited Trump to the White House on Thursday so they could begin to discuss the transition of power

Obama is due to deliver a statement from the White House with Vice President Joe Biden

President Barack Obama called to congratulate Donald Trump after his surprise victory, and invited him to a meeting at the White House.

A White House spokesperson said on Wednesday morning that the two men had spoken, and that President Obama had asked to president elect to travel to Washington DC on Thursday so they could begin to discuss the transition on power.

President Obama said the two men spoke at 3:30am on Wednesday.

The White House said in a statement: 'Ensuring a smooth transition of power is one of the top priorities the President identified at the beginning of the year and a meeting with the President-elect is the next step.'

That call came after President Obama's somber election night speech on Wednesday, during which he told Americans: 'No matter what happens, the sun will rise in the morning'.

Obama will also deliver a statement, with Vice President Joe Biden, from the White House's Brady Press Briefing Room at 12.15pm ET.

Big win: In a victory that has shaken the world, Donald Trump (pictured giving his victory speech) has swept to power on his promise to 'Make America Great Again'

Trump's campaign manager Kellyanne Conway also spoke about the call between the two men during an appearance on Today Wednesday morning, saying: 'Well, it was a very warm conversation.

'We were happy to receive the call from the President and they had a great, thorough conversation about Mr. Trump's victory, he was congratulated, and I think they resolved to work together, which is exactly what this country needs - to get the current president and the president elect and others who are in leadership position to help unify and heal the country.'

She then added: 'We expect that the two gentlemen will be meeting soon.'

White House press secretary Josh Earnest had told reporters traveling aboard Air Force One last week that the president was leaving his schedule open on Wednesday and Thursday for a possible meeting with the president-elect.

On Tuesday night, Obama said in a video message for Buzzfeed News: 'Let's face it. This has been an exhausting, stressful and sometimes downright weird election for all of us.

Forlorn: Mr Obama looked serious throughout his message, where he urged people to stay calm

'But here's what I want everybody to know: While we've certainly seen some new things this time around, what isn't new is that our democracy has always been rowdy and raucous. We've been through tough and divisive elections before and we've always come out stronger for it.'

He added: 'Remember, no matter what happens, the sun will rise in the morning and America will still be the greatest nation on earth'.

His message was downbeat - and in marked contrast with his buoyant mood on the previous night, where he and wife Michelle joined the Clintons and daughter Chelsea on stage at a final glitzy rally in Philadelphia.

On Tuesday night, Trump said that he had received a call from his opponent, Hillary Clinton. In his remarks to supporters, he praised her for a hard-fought campaign and said Americans owe her a major debt of gratitude for her long service to the country.

It came after the most divisive US presidential election in modern history ended and Trump swept to power and claimed his place as America's 45th president.

Contrast: The night before the Obamas and the Clintons looked buoyant as they attended a rally in Philadelphia - but polls showing she would win were wrong

OBAMA'S ELECTION NIGHT MESSAGE FOR AMERICANS This has been an exhausting, stressful and sometimes downright weird election for all of us. But here's what I want everybody to know: While we've certainly seen some new things this time around, what isn't new is that our democracy has always been rowdy and raucous. We've been through tough and divisive elections before and we've always come out stronger for it. That's what makes America special, the idea that while progress isn't guaranteed, each of us has the power to choose our path, not just on nights like this, but everyday in between. It is a beautiful and fragile gift and we should treat it that way. So whether your chosen candidates win or lose tonight, let's all agree not only to stay engaged, but to push ourselves to do even better. To vote not just when a president's on the ballot, but for Congress and mayor and school board and dog-catcher. To educate ourselves on the issues and to join with our neighbors in tackling the ones that face our communities. And, most importantly, to see each other not simply as Democrats or Republicans, but as fellow Americans. To treat each other with the respect and empathy and kinship that title, Americans, demands. That's especially true here on a place like Twitter, but it's something we can bring with us to everything we do online and off. We can choose to see the best in one another. Have a good night everybody. And remember, no matter what happens, the sun will rise in the morning and America will still be the greatest nation on earth. Advertisement

It is an astonishing victory for the celebrity businessman and political novice who capitalized on voters' economic anxieties, took advantage of racial tensions and overcame a string of sexual assault allegations on his way to the White House.

Trump's triumph over Hillary Clinton, not declared until well after midnight, will end the Democrat's eight years controlling the executive branch.

He will govern with Congress fully under Republican control and lead a country deeply divided by his rancorous campaign against Secretary Clinton.

He faces fractures within his own party, too, given the numerous Republicans who either tepidly supported his nomination or never backed him at all.

As he claimed victory, Trump urged Americans to 'come together as one united people'.

Secretary Clinton, who hoped to become the nation's first female president, called her Republican rival to concede but did not plan to speak publicly until Wednesday morning.

Trump, who spent much of the campaign urging his supporters on as they chanted 'lock her up', said the nation owed Mrs Clinton 'a major debt of gratitude' for her years of public service.

The Republican blasted through Democrats' long-standing firewall, carrying Pennsylvania and Wisconsin, states that had not voted for a Republican presidential candidate since the 1980s.