The 37-year-old actor made the announcement on her Instagram page and posted photo reading "It's a girl".
"I am beyond over the moon to share that our beautiful baby girl, Sadie Rauch, has arrived and our hearts are bursting at the seams with love for her.
"I will never take for granted the difficult road it took to get here. To those on that road: I'm sending you so much love today and always," Rauch posted.
This is the first child for the couple.