The Obamas selected artists Kehinde Wiley and Amy Sherald for the paintings, which take their place in the National Portrait Gallery's collection of presidential portraits.
Wiley and Sherald were the first black artists ever commissioned to paint a president or first lady for the Smithsonian.
For Obama's portrait by Wiley, the former president is depicted sitting in a brown chair with a backdrop of bright green leaves and colourful flowers. Sherald's painting of Michelle Obama shows her sitting with one hand under her chin and the other draped across her lap, while wearing a long flowing dress decorated with geometric shapes.
Obama, the first African-American US president, complimented Sherald for her portrait of Michelle.
"I want to thank you for so spectacularly capturing the grace and beauty and intelligence and charm and hotness of the woman that I love," Obama said.
He quipped that Wiley, who painted his portrait, was at a disadvantage because his subject was "less becoming."
"I tried to negotiate less gray hair and Kehinde's artistic integrity would not allow him to do what I asked," Obama said in tongue-in-cheek fashion. "I tried to negotiate smaller ears - struck out on that as well."
"I was anticipating - hoping for - a bolder, more incisive image of the strong-voiced person I imagine this former first lady to be," Cotter said in his review.
Most Twitter posts described the portraits as stunning, although a few criticized them as poorly executed.
"Behold the beauty of Barack and Michelle Obama's official portrait," tweeted @newyorknewart.
Michelle Obama said she hoped the portrait would have an impact on young girls of colour in the years ahead.
"They will look up and they will see an image of someone who looks like them, hanging on the wall of this great American institution," she said. "I know the kind of impact that will have on their lives, because I was one of those girls."
The Portrait Gallery's tradition of commissioning presidential portraits began with President George H.W. Bush. Other portraits were acquired as gifts, bought at auctions or through other means.