Trump said that the meeting was supposed to last for 10 to 15 minutes but went far longer.
"The meeting lasted almost for an hour and a half, and as far as I'm concerned, it could have gone on for a lot longer," Trump said.
"I very much look forward to dealing with the president in the future, including counsel," he added. "I look forward to being with you many, many more times."
Thursday night, Trump issued a rare post-election tweet from his personal account.
Trump visited the White House after receiving an invitation from Obama following Trump's surprise electoral victory Tuesday night.
Today's meeting was the first time the two men have ever met face to face, even though they've been talking about each other for years, during which Trump regularly questioned Obama's birthplace and whether he was a legitimate president.
After his White House visit, Trump went to Capitol Hill to meet with Republican leaders there including Speaker of the House Paul Ryan and Senate Majority Leader Mitch McConnell.
As he left McConnell's office, ABC News was able to ask what his first priority will be when he takes power.
"We have a lot of priorities -- really great priorities. People will be really happy," Trump said.
When asked to list his three top priorities, Trump said "immigration -- borders are important. Healthcare. Jobs -- big league jobs."
ABC News' Mary Bruce, Katherine Faulders and Ali Rogin contributed to this report.