The clip shows footage taken right before the two launched into the official interview, while Obama and Harry were still chatting about what they'd discuss and checking sound levels.
After the announcement of his marriage to American actor Meghan Markle, Prince Harry continues to demonstrate that his ties to American celebrities are only beginning to expand.
"Do I need a British accent?" a jovial Obama interrupts, asking whether he will have to speak more quickly.
Harry also told his interviewee that if he used long pauses between answers, he would probably get "the face".
"No, no, let's keep it this way", Harry said, laughing.More news: Peter Kay has cancelled his upcoming tour due to 'unforeseen family circumstances'
More news: There Used to be Human-Sized Penguins Roaming Around New Zealand
More news: Multiple NFL Network Employees Sued For Sexual Harassment, Demanding Oral Sex
"I don't want to see that face", Obama says.
That's what makes an upcoming, four-part series interview featuring Harry interviewing Barack so exciting. "I much prefer that".
The palace said the full interview will be made available as a podcast. "Because I'm a slow speaker", the former president asked the prince.
Kensington Palace said the chat, part of Harry's guest editorship of the show, was recorded in Toronto in September during the Invictus Games.
Last year Mr Obama and his wife, Michelle, posted a mock challenge to Prince Harry on Twitter before the 2016 Invictus Games, telling him to "bring it".