Miller, who was seen on Broadway in After Miss Julie, gave birth to a girl. The West End actress and Sturridge have been dating for over a year.
Miller, who was also seen in the West End production of Flare Path, appeared in the films "Stardust," "G.I. Joe: The Rise of the Cobra," "Casanova," "Factory Girl" and "Alfie," among others. As previously reported, she will star in the upcoming BBC2 drama "The Girl."