The couple chose to name their son Moroccan Scott Cannon after the Moroccan-inspired decor of the top tier of Carey's New York City apartment.
The so-called Moroccan Room is also where Cannon proposed. They picked the middle name Scott since it's both Cannon's middle name as well as his grandmother's maiden name.
The couple named their daughter Monroe Cannon after Marilyn Monroe, who has inspired Carey. Unlike her brother, Monroe doesn't have a middle name because Carey doesn't have one either.
Carey and Cannon's twins were delivered Saturday in Los Angeles.
The pair got married in 2007 after a whirlwind romance.