Obama offered to do everything he can to help the New York businessman succeed when he takes office.
Sitting next to the Democratic president in the Oval Office, Trump told reporters: "We really discussed a lot of situations, some wonderful, some difficulties." He said Obama explained "some of the great things that have been achieved," but did not elaborate.
Trump, elected on Tuesday to his first public office, said he looked forward to more meetings with Obama. He noted it was the first time the two met face-to-face, and the White House said the meeting occurred with no staff present.
Obama offered to do everything he can to help the New York businessman succeed when he takes office on Jan. 20 and urged the country to unite to face its challenges.
"We now are going to want to do everything we can to help you succeed because if you succeed, then the country succeeds," Obama said at the end of the meeting.
The relaxed, cordial demeanor between Obama and Trump in front of the cameras was in stark contrast to the months of harsh rhetoric that came from both during a bitter election campaign.
Trump used Obama as a punching bag during his campaign speeches, repeatedly calling the president's policies - from healthcare to an Iran nuclear deal - a "disaster."
For his part, Obama and first lady Michelle Obama attacked Trump as being unfit to hold the office of president.
But immediately following Trump's unexpected election victory over Democratic rival Hillary Clinton, the tone changed.
On Wednesday, Obama said that despite his major differences with Trump, he would follow the lead of former Republican President George W. Bush in 2008 and ensure a smooth handover to Trump.
In a possible pivot by Trump, controversial campaign proposals, including his call to ban Muslims from entering the United States, have been removed from the president-elect's campaign website.
As the current president and next president huddled, White House chief of staff Denis McDonough was seen walking near the Rose Garden with Trump's son-in-law Jared Kushner, who like Trump is also a real estate developer, and other aides.