It will be a very happy holiday for Claire Danes and Hugh Dancy!

The Homeland star, 33, and her actor husband welcomed their first child, son Cyrus Michael Christopher Dancy, on Monday, Dec. 17, her rep confirms to PEOPLE exclusively.

Since confirming her pregnancy in July, Danes has stayed mostly mum on the subject of baby — including keeping the sex a secret — but tells PEOPLE in its new year-end double issue that she looks forward to “getting to know our new Dancy” over the break.

Danes, who won an Emmy in September for her role as bipolar CIA-agent Carrie Matheson on the hit Showtime drama, wed Dancy, 37, in a private ceremony in France in 2009.