"It's a girl. The tiny new empress of my everything . She's immaculate. We're delirious," Gillies tweeted Sunday.
He did not mention the child's name or exactly where and when she was born.
Cook, a cast member of the TV series "Perception," married Gillies, star of "The Vampire Diaries," in 2004.
Interpol investigating stolen passports on missing flight
Teacher apologizes for showing sexual image of herself in class