Actors Rachael Leigh Cook, Daniel Gillies Welcome Baby Girl

"It's a girl. The tiny new empress of my everything . She's immaculate. We're delirious," he writes.

The couple — who announced they were expecting in May — were married in 2004, but it was only recently that the Perception star, 33, and Gillies felt ready to bring a baby into the mix.

"We're both people who like kids, but we weren't jumping up and down, like, 'Oh my God, let's start that chapter of our lives,'" Cook told PEOPLE in June. "There was just so much more both of us wanted to do."