The former Doctor Who actress welcomed her first child with husband Laurence Fox into the world at London's Portland hospital, after having a caesarean section on Tuesday.
At the time of writing no other details about the birth had been revealed. The 26-year-old actress - who was accompanied by Laurence, 29, at the hospital - recently revealed she was feeling nervous about the birth, and had become obsessed with having scans.
She said: "Some women are all about this glowing, blooming thing, aren't they? I haven't really tapped into that. I've basically replaced all my vices for a new one - control.
"I've had about 10 scans and I bought one of those baby heart monitor things. Such a bad idea - it's like listening to a huge shell on the beach. But I do love it. The whole thing is just so sweet, tender and adorable." Billie recently revealed she has no intention of raising a child in the US, despite the success of her TV show 'Secret Diary of a Call Girl' in the country.
She said: "Going to the US is a load of b******s. For the moment, I'm just going to focus on being a mum and that's kind of a relief because I don't have to think about the rest of my career."