Actress Milla Jovovich gave birth to a baby girl Saturday morning at L.A.'s Cedars Sinai Medical Center, sources tell Usmagazine.com.

It is the first child for the Russia-born Jovovich, 31, and her fiance, director Paul Anderson, 42. A source confirms to Us that the couple has named their daughter Ever. "Everything went really smooth," says the source.

Jovovich hosted a baby shower at her Beverly Hills home on Oct. 14, where the yoga enthusiast gifted friends with special oils and Express sweatpants. "She couldn't wait for the baby to come," a source at the shower told Us.

The couple has said they plan to marry after the birth.

“He got me an antique ring and he proposed four years ago, but we broke up in between,” the Jovovich-Hawk clothing designer explained to Us last April. She and Anderson, 42, have been dating since he directed her in 2002's Resident Evil.

A rep for Jovovich couldn't be reached for comment.