The 'Homeland' actress and her British actor husband Hugh Dancy welcomed their first child, Cyrus Michael Christopher Dancy, into the world on Monday 17 December 2012.
A spokesperson for the Emmy award-winning star confirmed news of the baby's arrival to People magazine.
The 33-year-old blonde beauty confirmed her pregnancy in July and revealed she was determined to keep the baby's sex a secret.
Claire also said she was looking forward to taking a break over the festive season and "getting to know our new Dancy".
Claire married Hugh, 37, in 2009 at a private ceremony in France, and recently revealed she confides everything in the actor, even though they have been forced to spend a lot of time apart because of their respective work commitments.
She said: "I haven't been spending a lot of time with Hugh lately because we've been in so many different places with work, but he is the person I tell absolutely everything to. I trust him more than everyone else.
"A couple of weeks ago I went on a date night with Hugh, who I hadn't seen in a long time because of work. We went out to a restaurant in New York and I had a big bowl of pasta. I was a little overwhelmed with joy to be with my guy, eating lots of carbs. It was heaven."
Congratulations Claire and Hugh and a warm welcome to baby Cyrus!
FemaleFirst @FemaleFirst_UK
Tagged in Hollywood Parenting Claire Danes Hugh Dancy Baby news Homeland Baby