Billie's husband Laurence Fox announced the couple's happy news with the tweet: "One born every minute. We had our minute today. Couldn't be happier. Beautiful boy. Everything fine."
The couple - who are already proud parents to three-year-old Winston - have named their new arrival Eugene Pip.
Billie's pregnancy was revealed back in October by the artistic chief behind her new play, Neil LaBute's Reasons To Be Pretty.
One born every minute. We had our minute today. Couldn't be happier. Beautiful boy. Everything fine.
- Laurence Fox (@LozzaFox) April 5, 2012
"She was upset and told me she was pregnant," Michael Attenborough, the Almeida theatre's artistic chief revealed. "However, she was Neil LaBute's and my first choice for the part - and fortunately the character is pregnant - so with a bit of judicious re-writing we're all delighted she'll be with us."
Speaking after Winston's birth, Billie said she was undecided about having more children, saying: "I used to want a big family, but now I am wondering if it would be OK if Winston was an only child!
"Seriously, I would like to have three children. I'm thinking of having two close together and leaving it a while, then having another."
Congratulations Billie and Laurence!