Weisz gave birth, and according to multiple outlets, the actress and her husband of seven years are said to be "very happy" with the latest addition to their family.
The couple's newborn joins Weisz' son Henry, 11, who she shares with ex Darren Aronofsky, while Craig shares daughter Ella, 25, with ex-wife Fiona Loudon.
Back in April, Weisz shared her joy about the impending arrival of her bub.
Talking to the New York Times, "Daniel and I are so happy. We're going to have a little human. We can't wait to meet him or her. It's all such a mystery."
Days later, Weisz debuted her baby bump on April 23 in a Sonia Rykiel knit maxi dress while out and about in New York City.
Weisz and Craig, 50, married in 2011, just six months after they began dating.
The star also opened up about the pair’s relationship to the Times, saying, “I’m very happy being married, very, very happy.” She mused of the couple’s reserved nature when it comes to their romance, “We’re just really crap at talking about our private lives.”
Earlier this year, Weisz told the Evening Standard that she “never thought” she’d get married before meeting Craig.
“It was not an ambition of mine. It was the opposite. I couldn’t relate to romantic comedies — marriage seems to be the whole point of them. Then it just happened, happily, at a more mature moment,” she said.
Further asked if she thought marriage had changed her, Weisz told the Evening Standard, “I mean, I wear a ring all the time. I wear my ring with pride. I’m taken.”