Angelina Jolie, 31, has collected the boy from a Ho Chi Minh City orphanage.
Jolie and Pitt visited Ho Chi Minh City last November, where they first met children at the Tam Binh orphanage.
Nguyen Van Trung, the director of the orphanage, said it was an emotional moment when she left with her new three-year-old son.
"They tried to make friends with the Vietnamese boy, who cried when he saw them because for him, they are strangers," he told reporters. "Jolie was very moved. Both of them tried to comfort the little boy," he added.
The boy has been living at the orphanage since he was abandoned as a baby, but if all goes to plan officials have said that Jolie can take him home by the weekend.
Angelina has already adopted two children and last year she gave birth to a daughter with her partner Brad Pitt.