He made reference to the false ‘birther’ conspiracy led by President Trump which questioned his citizenship and eligibility to serve. Mr Obama, who was born in Hawaii to an American mother and a Kenyan father, served from 2009 to 2017 as the first African-American president in US history.
President Trump, who is entering his final days in the White House, dropped the controversial stance during his bid for power in 2017 as it became a distraction to campaigning.
Mr Obama, 59, released a longer version of his birth certificate in response to those who suggested he was not born in the US.
Conspiracy theorists known as ‘Birthers’ claimed he was actually born in Kenya and therefore had not been eligible to stand as president.
The US Constitution states an American leader must be a natural-born citizen.
Mr Obama appeared in a socially-distanced interview on The Daily Show on Tuesday night.
The late-night show’s host Trevor Noah praised the 44th US president’s ability to roast people – but asked whether he’d be more careful in the future as his roastees have a habit of running for office.
Mr Noah, a South African, referenced his roasts of President Trump and Kanye West, who announced his own presidential election bid in July.
Obama replied: “Well I should roast people I admire more.
In the 2011 speech, he said: “The state of Hawaii released my official long form birth certificate.
“Hopefully this puts all doubts to rest, but just in case there are any lingering questions, tonight, I’m prepared to go a step further.
“Tonight, for the first time, I’m releasing my official birth video.”
He then played the opening sequence of the Lion King to the audience, who burst into laughter and applause – apart from Mr Trump.
Mr West was called a “jackass” by Mr Obama after he famously interrupted Taylor Swift at the 2009 MTV Video Music Awards.
On Monday, Joe Biden officially won the US Presidential election after the Electoral College finalised the result.
He will be sworn in on January 20.
President-elect Biden, speaking after the finalised result, said the “will of the people prevailed”.