According to People, Russell gave birth earlier this month. As of now, no details on the baby's gender or name have been released.
Russell and Rhys, who play married KGB spies on the FX drama, confirmed they were dating in April 2014. The pregnancy was not written into the show, which was renewed for its final two seasons last week.
Russell, 40, was previously married to Shane Deary, with whom she has two children, daughter Willa, 4, and son River, 8. This is the first child for Rhys, 41.