Barack Obama pledges to ensure a smooth transition for his successor Donald Trump

Congratulating President-elect Donald Trump on his election victory, President Barack Obama said the nation is now "rooting" for his success in uniting and leading the country. Obama also pledged to ensure a smooth transition for his successor.

"I know everybody had a long night. I did as well. I had a chance to talk to President-elect Trump last night at about 3:30 in the morning to congratulate him on winning the election and I had a chance to invite him to come to the White House tomorrow and to talk about making sure there is a successful transition between our presidencies," Obama said in his first remarks on the election results from the White House's Rose Garden.

Joined by Vice President Joe Biden, Obama said it is "no secret" that Trump and he have "some pretty significant differences".   

"But remember eight years ago President (George) Bush and I had some pretty significant differences. But President Bush's team could not have been more professional or moregracious in making sure we had a smooth transition so that we could hit the ground running.

"One thing you realise is that the Presidency and the Vice-Presidency is bigger than any of us. So I have instructed my team ...to work as hard as we can to make sure this is a successful transition for the President-elect," he said.

"We are now all rooting for his success in uniting and leading the country. A peaceful transition of power is one of the hallmarks of our democracy," he said.

Earlier Obama called Trump from his residence in the White House to congratulate him.

Trump campaign manager Kellyanne Conway also said Obama called Trump while he was speaking to his supporters in New York, and so Trump called him back after he left the stage.

She said the two leaders had a "very nice talk."

Conway said they would meet possibly on Thursday.

In a stunning result, billionaire businessman Trump beat seasoned politician Clinton in the knife-edge polls, defying the odds to become the 45th US President after starting off as a rank political outsider.