The 30-year-old actress and U.N. activist says the girl's full name is Zahara Marley Jolie. Jolie won't divulge the child's age, weight or height, but she tells PEOPLE that she and Maddox, the 3-year-old son she adopted from a Cambodian orphanage in 2002, are "very happy to have a new addition to our family."
The head of Ethiopia's state-run adoption agency, Hadosh Halefom, tells the Associated Press: "The paperwork has gone through. Miss Angelina's request was accepted last week."
Hadosh also says Jolie met 10 conditions for adopting a child from Ethiopia, including a financial evaluation. "Although she is a film star, she still has to meet the same requirements as everybody else."
Jolie has often talked of adopting a second child. After a trip to Ethiopia earlier this year, Jolie said of Maddox: "My son is in love with Africa, so he has been asking for an African brother or sister."
As for rumors that Jolie and Brad Pitt are planning a family together, the source denies them. "This has nothing to do with her relationship with Brad Pitt. People are going to try to say it's about their relationship. But it's not. Angelina's adopting as a single mother, and she wants that emphasized."