Obama told reporters that he and Trump had an "excellent" conversation about US foreign and domestic policies.
"We talked about foreign policy, we talked about domestic policy," the president said.
Trump indicated he would hold more meetings with Obama.
"I very much look forward to dealing with the president in the future, including council," Trump said at the White House. "I look forward to being with you many…times in the future."
White House spokesman Josh Earnest told reporters the two discussed staffing and organizing the White House during their first meeting.
"That is complicated business," Earnest stated. "Any White House is expected to be structured in a way to deal with multiple challenges or even multiple crises at the same time."
Trump's surprise victory over Democrat Hillary Clinton in the US presidential elections on Tuesday caught many by surprise. His divisive rhetoric on the campaign trail prompted tens of thousands of people to protest his election in cities across the US on Wednesday.
