Milla Jovovich, Paul Anderson Have Daughter
11/04/2007 AT 05:00 PM EST
The baby, born at the Cedars Sinai Medical Center in Los Angeles, weighed in at 7 lbs., 8 oz.
"Parents and baby are doing fine," says their rep.
Anderson, 42, produced and wrote three Resident Evil movies starring Jovovich, 31.
The couple met in 2002, when Anderson, whose films also include Alien Vs Predator, directed Jovovich in the first Resident Evil.
They announced their engagement in March 2003, but have not yet announced a wedding date.
In terms of fashion, the Ukranian-born Jovovich and partner Carmen Hawk have their own label, Jovovich-Hawk, which recently unveiled a collection for the European retail chain Mango.
After her pregnancy was announced, Jovovich told PEOPLE: "I'm gaining weight, which is fun. "I've been craving lots of bad stuff but I've been cooking a lot. I did this amazing slow-roasted tomato dip the other night, and steaks, and, oh, I've been eating my mom's potatoes – I know how to make my mom's potatoes – like crazy. It's awful. I have to stop."