The Trump-Obama meeting was unexpected just days ago.
It would be recalled, during the campaign, Mr Obama had called Mr Trump “uniquely unqualified”, but now has has said he is “rooting” for him after his shock defeat of Hillary Clinton.
The Republican president-elect had also in reprisal questioned Mr Obama’s US citizenship and vowed to dismantle his legacy.
But in the immediate aftermath of Tuesday’s results, Trump and Obama have both sought to set politics aside ahead of the transition.
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After his meeting with Obama, Trump will meet with House speaker Paul Ryan at the Capitol Hill Club and majority leader Mitch McConnell at Capitol Hill.
The area around the White House is swamped by journalists at the moment hoping to catch a glimpse of President-elect Trump, but it was a very different scene on Wednesday night.