The 'We Belong Together' singer and America's Got Talent host Cannon welcomed a son and a daughter at a Los Angeles hospital over the weekend.
The boy has been named Moroccan Scott Cannon, while the girl is called Monroe Cannon, according to a post on Carey's official website.
The name Moroccan is in reference to the decor of a room in Carey's New York apartment, which is influenced by the country and also served as the setting for Cannon's proposal, while Scott is Cannon's middle name, says CNN.
Monroe is a tribute to the late Marilyn Monroe.
Carey had previously teased on Twitter that the children had both been given names beginning with 'M', inviting followers to guess the monikers. She also described the newborns, who arrived on her third wedding anniversary to Cannon, as "incredible gifts".
The couple, who married in the Bahamas, renewed their vows in the hospital with Reverend Al Sharpton shortly following the birth of their twins.