People magazine reported Saturday that the twins' names are Dexter Henry Lorcan and Frank Harlan James, according to a rep for the couple, who also said, "Mother and sons were doing splendidly."
Krall, 42, told People she was "genetically disposed to a double delivery," that there are twins on her side of the family. These are Krall's first children; the London-born Costello already has one child.
Adding to the joy, Costello, 52, nabbed a Grammy nomination for best pop album for "The River in Reverse," which he wrote with Alain Toussaint.
Celebrity Families of 2014 [PHOTOS]