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The Oscar-winning actress collected the boy from a Ho Chi Minh City orphanage on Thursday. He has been renamed Pax Thien Jolie, which reportedly means "peaceful sky".
Vietnamese authorities advise that Jolie will be able to take her son back to the US by the end of the week.
She already has two adopted children, five-year-old Maddox and two-year-old Zahara. Last year she gave birth to a daughter, Shiloh, by her partner Brad Pitt.
Jolie filed adoption papers in Vietnam as a single parent because she and Pitt are not married.
