Barrack Obama said he was "encouraged" by their "excellent" and "wide-ranging" conversation, lasting over an hour.
During the election campaign, Trump vowed to dismantle Obama's legacy and he has previously questioned his US citizenship.
Obama, meanwhile, had called Trump "uniquely unqualified".
But following Trump's shock defeat of Hillary Clinton in Tuesday's election, Obama appealed for national unity and said he was "rooting" for him.
After Thursday's behind-closed-doors meeting in the White House, Obama said: "My number one priority in the coming two months is to try to facilitate a transition that ensures our president-elect is successful."
He said they had discussed domestic and foreign policy and he had been "very encouraged" by Trump's interest in working with President Obama's team on issues facing the US.
Tump said he would "very much look forward" to dealing with President Obama in future.
"I have great respect, the meeting lasted for almost an hour and a half, and it could've, as far as I'm concerned, it could've gone on for a lot longer," the president-elect said.
"We discussed a lot of different situations - some wonderful and some difficulties."
As president-elect, he is entitled to get the same daily intelligence briefing as President Obama, which includes information on covert US operations and other data gathered by America's 17 intelligence agencies.
Mr Trump's team is understood to be focused on quickly filling key national security posts.
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