Baby Girl for Heath Ledger, Michelle Williams
In April, when PEOPLE reported on the pregnancy, Williams, 25, had been spotted attending prenatal yoga classes in Australia.
Ledger, 26, who most recently appeared in The Brothers Grimm and the skateboard movie Lords of Dogtown, split from actress Naomi Watts, a fellow Aussie, in April 2004.
Ledger and Williams costar with Jake Gyllenhaal in director Ang Lee's soon-to-be-released gay cowboy romance, Brokeback Mountain, for which Ledger received near-unanimous raves on the film-festival circuit.
As Gyllenhaal tells PEOPLE: "Heath wears his heart on his shoulder. (With) that kind of sensitivity and strength his child will feel safe."