Mr Trump, who has described himself as Mr Obama's "worst nightmare," told the president he was "a very, very good man."
On the campaign trail he repeatedly described him as weak, "a disaster," ineffective and "the most ignorant president in our history.”
On Thursday, however, both men struck a conciliatory note after they met to discuss the transition from one administration to the next.
"We want to do everything we can to help you succeed, because if you succeed we all succeed," said Mr Obama.
There circumstances of the meeting were extraordinary. Mr Trump spent years claiming Mr Obama was born outside the US and was therefore not a legitimate president, while Mr Obama savaged him throughout the campaign as irresponsible and dangerous.