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Boys Dexter Henry Lorcan and Frank Harlan James were born in New York City, according to a rep for the couple, who adds, "Mother and sons are doing splendidly."
Krall and Costello said in a statement, "We are ecstatic!"
The babies are something of a third-anniversary gift for Krall, 42, and Costello, 52, who wed in London on Dec. 5, 2003.
In September, Krall told PEOPLE she's genetically disposed to a double delivery: "I have twins on my mother's side as well."
And she knew even then that she wouldn't dress her kids up in matching outfits: "Nah," she said with a laugh, "I won't be doing that."
JOSH & FERGIE: ROCKED BY SCANDAL
Did he cheat with a stripper?
Married less than a year, the couple denies an Atlanta woman’s claims that she and Josh had a fling
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