The first song the two belted out was a cover of "Signed, Sealed, Delivered," a song the first lady said is among her top favorites.
Obama revealed that filming the segment was just the second time in 7 1/2 years that she sat in the passenger seat of a car, the other time being when one of her daughters took a drivers ed course.
"I'm going to miss the people … they help you … they love you, to walk away from people you see every single day, that's going to be hard," Obama said of her time in the White House.
One of the highlights of the special was the duo's spirited performance of "Single Ladies" by Beyonce.
"We were making honey to put in our lemonade," Obama said with a smile when the two finished their ride. As they drove around the White House service roads, Corden's car was trailed by Secret Service agents.
They were later joined by rapper Missy Elliott for a performance of her song "This Is For My Girls," which was released in 2016, and written and recorded for Michelle Obama's Let Girls Learn initiative.
"It happened so fast — literally Kelly Clarkson was singing her part in Nashville while we were almost mastering it," the song's writer told told Billboard in 2016. "So we dropped her vocals in. It was that crazy."
Corden and Obama took advantage of Elliott's presence to launch into a spirited rendition of her hit, "Get Ur Freak On."
When Corden flipped back to the studio, he gushed about his experience in Washington, D.C.
"How cool is the first lady, Michelle Obama?" Corden asked at the end of the segment.