The twins - a boy and a girl - were born in a Los Angeles hospital on Saturday, on the couple's third wedding anniversary.
An announcement on Carey's official website on Wednesday said that her daughter is named Monroe Cannon, after Hollywood icon Marilyn Monroe.
Carey said the late actress has been a lifelong inspiration, adding that she bought a white piano that once belonged to Monroe at an auction several years ago.
The announcement said her son is named Moroccan Scott Cannon, explaining that Scott is Cannon's middle name, as well as his grandmother's middle name.
The babies are the first for Carey, 41, and comedic actor Cannon, 30, who married in 2008. Carey, the Grammy award-winning singer of hits including We Belong Together suffered a miscarriage shortly after her marriage.
Carey said in a Twitter message on Tuesday that the babies were "doing great and they are the most incredible gifts we could ever have imagined!", and thanked friends and fans around the world for their well wishes.
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