The new arrival, who weighed 5lb 12oz, made her entrance on Tuesday night.
"Samantha Burke is overwhelmed with joy at the arrival of her beautiful and healthy baby girl," the 24-year-old's spokeswoman told US publication People. "The baby and mom are doing wonderful."
There was shock in celeb circles two months ago when Jude confirmed he was expecting a child with the American brunette, whom he apparently met while filming Sherlock Holmes in New York.
His publicist said at the time: "Mr Law is no longer in a relationship with the individual concerned but he intends to be a fully supportive part of the child's life."
Thirty-six-year-old singleton Jude is already dad to sons Rafferty, 12, and Rudy, six, and his eight-year-old little girl Iris with his ex-wife Sadie Frost. He also has a stepson, Finlay, who is 18.
Not much is known about Samantha, who set up a blog to "share who I really am with you".
She recently wrote: "So, if you are so interested in the story of this 'ordinary' woman having a 'celebrity's' child, then read on."
In one entry she defends herself against accusations that she is a "golddigger".
"When I found out I was pregnant I was scared like any other single female would be," she writes.
"I didn't jump for joy because I 'hit the jack pot', I cried my eyes out and started adjusting my future plans in my head… Never once did I think about the money".