Sons Dexter and Frank are the first children for the married singers

Singers Diana Krall and Elvis Costello welcomed twins on Dec. 6, PEOPLE has learned.

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.”