Government officials said the boy was renamed Pax Thien Jolie and is almost three-and-a-half years old.
The adoption will be final once US embassy officials in Hanoi approve the paperwork. Jolie and Vietnamese officials have already signed adoption documents in Ho Chi Minh City.
"Everything went really well. It was a successful event this morning," said Nguyen Van Trung, director of the Tam Binh orphanage in the city, the communist-run Southeast Asian country's largest urban area with 8 million people.
"All she needs to do now is to travel to Hanoi to get the travel paperwork from the US embassy for the boy."
Senior officials said Jolie's adoption had been speeded up, partly due to her celebrity status.
The child had been registered as Pham Quang Sang at the orphanage. Trung said the boy had been abandoned at birth at a local hospital and has been at the orphanage since 2003.
Jolie took the boy with her to the Justice Department building in the city centre to sign the adoption documents. Her car left half an hour later.
"She was very beautiful. She signed and had her photo taken," department official Dao Van Tran said outside the building.
Jolie has two adoptive children and a biological daughter with partner Hollywood heartthrob Brad Pitt.
She flew into the southern Vietnamese city on yesterday night from Japan on a chartered plane. Her son Maddox and daughters Zahara and Shiloh Nouvel accompanied her.
Jolie, 31, filed adoption papers in early March through an unidentified American agency without Pitt because under Vietnamese law, an unmarried couple may not adopt a child. Single people may adopt children under the law.
In Vietnam, adoptions have been known to take as little as one month if background checks and issues of whether the adopting family can support a child are quickly resolved.
However, the process can take six months or longer in some cases.
Jolie and Pitt visited Ho Chi Minh City last November and met children at the orphanage.
The couple say they have no plans to marry but are committed to raising their children together. Their biological daughter, Shiloh Nouvel, was born last year.
Jolie adopted Maddox from Cambodia and Zahara from Ethiopia before her relationship with Pitt, who has now become their adoptive father.
The couple starred in the 2005 movie "Mr & Mrs Smith". They are also working together on the film "A Mighty Heart" about the killing of a US journalist by Pakistani militants.
Jolie won an Oscar in 1999 for best supporting actress in "Girl, Interrupted". She starred in the 2001 movie "Tomb Raider" which was filmed in Cambodia.