Their son was named Moroccan Scott Cannon after the top floor of Carey's New York apartment which has a Moroccan-inspired d?cor. The so-called Moroccan Room is where Cannon proposed to Carey in April 2008. Scott was chosen because it's both Cannon's middle name and his grandmother's maiden name.
The couple named their daughter Monroe Cannon after Marilyn Monroe, who Carey said inspired her. They did not give her a middle name, like her brother, because Carey doesn't have one either.
Carey, 41, gave birth to the twins on Saturday at an undisclosed hospital in Los Angeles.
The couple got married in 2008. They renewed their vows on Sunday, one day after the birth of their twins.
The Associated Press contributed to this report.