The 42-year-old actor's representative said: "I can confirm the arrival of Jude Law and Catherine Harding's daughter. Both are delighted and continue to ask that their privacy and that of their child be respected."
Singer Catherine, 23, - who also goes by the name of Cat Cavelli – became pregnant last summer, while spending six weeks with the star on location in the Czech Republic.
Their happy news was revealed in October, with a spokesperson saying: "I can confirm that Jude Law and Catherine Harding are expecting a child together in the spring.
"Whilst they are no longer in a relationship, they are both wholeheartedly committed to raising their child."
Catherine' close friend and model Laura tweeted a link to the news, writing: "Congratulations to my best friend @CatCavelli on expecting her new baby. Can't wait xx."Friends close to the singer told the Daily Mirror she was 'delighted' by the prospect of becoming a mother, despite being separated from Jude.
A source close to Cat told the paper: "It all happened very quickly. They met a little while ago and fell for one another, then Cat told friends that she was going out to Prague, that's when it emerged that she was in a relationship with Jude."
The actor also has a five-year-old daughter, Sophia, with American model Samantha Burke following a brief fling in 2008, and three children - Rafferty, 18, Rudy, 12, and Iris, 13 - with his ex-wife Sadie Frost, with whom he shares custody.