The 33-year-old actress gave birth to a boy, Knox Leon, and a girl, Vivienne Marcheline, by Caesarean section about 8 p.m. Saturday in Nice in southern France. Jolie had a local anesthetic and was conscious throughout, the doctor said.
Pitt was in the delivery room at the seaside Lenval hospital as the babies were born one minute apart, Sussman said, the boy weighing just over 5 pounds and the girl 5 pounds.
"He was perfectly calm and everything went well," Sussmann said.
"He was very happy ... The emotion was very strong for him," the doctor added. "Angelina Jolie was speaking, was laughing with her husband. They were happy."
"The mother, the babies, the father are doing marvelously well," he said.
Sussmann said the Caesarean was moved forward from its originally planned date "for medical reasons" so the babies could be born "in the best conditions." The doctor did not give details.
He said Jolie is expected to stay in the hospital for a few more days and that she now needs rest. The four other Jolie-Pitt children -- Maddox, 6; Pax, 4; Zahara, 3; and Shiloh, 2 -- have not yet seen their new sister and brother, he added.
The doctor said he believed the baby girl's middle name was chosen in honor of Jolie's mother, actress Marcheline Bertrand, who died in January 2007 after a 7 1/2-year battle with cancer.
Jolie had checked into the hospital late last month to rest and be monitored by her doctor before the birth.
Before that, she, Pitt and their children had moved into a large estate, Miraval, in the French hamlet of Correns, which is just a short helicopter ride from the hospital. Correns is about 60 miles from Nice, a resort on the Mediterranean.
Though the lenses of the world's paparazzi had been trained on maternity wards across the French Riviera, Jolie managed to slip unobserved into the clinic, which has magnificent views of the Mediterranean, reportedly arriving by helicopter on the hospital's rooftop helipad.
Pitt was seen coming and going after Jolie's hospitalization became public.
The first photos of the new twins are expected to fetch millions of dollars.
Paparazzi and curious sightseers gathered outside the hospital in Nice on Sunday, hoping for glimpses and shots of Pitt.
Local newspaper Nice Matin, which first broke news of the birth, reported Sunday that the couple have sold rights for the first photo of their newly enlarged family to a U.S. publication, which it did not name, and that the proceeds would go to charity.
The newspaper gave no source for that information. But the doctor said the couple decided to announce the birth to Nice Matin first because of its links to Nice. The newspaper called the twins "the most famous babies in the world."
Earlier in the week, the hospital said it had coated the windows of Jolie's room with a special material to prevent paparazzi from taking unauthorized pictures of the star couple.
Tourists and residents of Nice, a popular resort, welcomed news of the birth. The city's mayor, Christian Estrosi, visited the hospital Sunday to deliver the twins' birth certificates -- which spared Pitt the need to go to City Hall himself to register the babies, and run the gauntlet of the photographers waiting outside.
"It's a happy day for Mrs. Angelina Jolie and all the citizens of Nice," said Estrosi.
The mayor previously has said that the twins will always be considered honorary citizens of the city, regardless of whether they opt to obtain French citizenship.