Julia, 34, gave birth on Monday to a little girl named Carey – after her maiden name.
JUSTIN TIMBERLAKE'S WIFE JESSICA BIEL 'PREGNANT WITH THEIR FIRST CHILD'
The couple also have son Max, 3, together, and James, 36, previously spoke out about how parenthood has changed him.
Former Gavin and Stacey star James lost five stone after Max's birth, and said: "It has given me a sense of clarity."
But that moment of clarity didn't happen straight away. In 2011, James told a UK radio station: "For a while it's nothing but annoying and then slowly and surely in around three months when you get a smile you go, 'Aww, actually you're all right'.
"Let's be honest – I'm fed up of these guys who go, 'Aww! The minute I held it in my arms, I knew I'd jump in front of a bus for you.'
"No you didn't. A parked bus maybe."
Julia and James married in a lavish ceremony in September 2012, following his Christmas day 2010 proposal.