Angelina Jolie and Brad Pitt have signed a long-term lease for a chateau on the French Riviera, according to reports.

The couple, who have four children and two more on the way, signed a three-year lease on the 880-acre estate called Chateau Miraval, where neighbors will include Johnny Depp and David and Victoria Beckham, according to the French newspaper Nice Matin.

The estate, reportedly valued at $70 million, comes with its own vineyard, olive groves, lake, moat, 20 fountains and even a forest to help ensure privacy.

source told E! Online. “No one will ever be able to get pictures of them relaxing at home, it’s just impossible.”

At the Cannes International Film Festival, Jolie, 32, who is expecting twins this summer, told reporters that she was thinking of giving birth in France, and that French is the “second language” in the family’s home.

A rep for Pitt and Jolie had no comment on the estate.

Angelina Jolie and her twins left the hospital early Saturday - a week since she gave birth to Knox Leon and Vivienne Marcheline.

“Angelina Jolie left the Clinic Santa Maria of Fondation Lenval early in the morning of July 19th,” hospital rep Nadine Bauer confirmed to PEOPLE. “The mother and babies are doing very well.”

There were only a few journalists camped outside the Fondation Lenval hospital in Nice, France, early Saturday morning but even they didn’t know for sure when Jolie slipped out of the hospital with her twins at 4 a.m. local time.

Jolie and the newest Jolie-Pitts left Lenval to join their excited siblings - Maddox, 6; Pax, 4; Zahara, 3; and Shiloh, 2 - at Chateau Miraval, the enormous and luxurious chateau in Correns, France, that Jolie and partner Brad Pitt rented in May.

“We saw the cars and we thought it was her but we didn’t see anything,” one observer said.

Photographers had been stationed on nearby roofs of the hospital, hoping that Jolie would leave as she had arrived nearly three weeks ago - by helicopter.

Bauer added Saturday that hospital staff wanted to thank their own personnel for the attention and care they gave the Jolie-Pitt family. She also released a statement from the hospital, which thanked “those journalists around the hospital who did their best to respect their privacy.”

SECRET GETAWAY

Jolie’s departure began at about 3:50 a.m. when, according to an eyewitness, a grey Volkswagen minibus with darkened windows arrived outside the hospital on its Promenade des Anglais.

“There was a sudden spray of light out of the hospital’s garage way and then four or five people came out of that through a rear doorway,” the witness said. “They stood behind the hospital in a small courtyard in the dark.”

The courtyard entrance, a gated area for emergency access has been closed during Jolie’s stay, “was suddenly opened by someone who was waiting in the bus stop beside the hospital,” the witness said. “This group of people got into the van, very quickly. . . . It was all done in a hurry. And they were very quick organizing themselves inside. Very rapid. And then ‘Pouf!’ they were gone.

“With all the press attention around them, a constant watch on the front of the hospital, they managed to leave so quickly, my hat’s off to them,” the witness added.

At 9 a.m., Dr. Michel Sussmann, who delivered the twins by Cesarean section on July 12, confirmed the family’s departure, telling reporters, “You can go home. The story is over.”

Added Bauer: “We enjoyed having her and her family here very much.”

Just hours after he cut the umbilical cords of his newborn twins, Brad Pitt welcomed the mayor of Nice and told him, “I’m the happiest father ever.”

In fact, the proud papa kept repeating the phrase over and over again, Mayor Christian Estrosi - who visited Pitt and Angelina Jolie in their hospital room - told the local newspaper Nice-Matin.

The twins, Knox Leon and Vivienne Marcheline, were born Saturday and the mayor came by the next day to sign their birth certificates.

The actress’s obstetrician, Dr. Michel Sussmann, also said that Knox and Vivienne - who weighed in at 5.03 and 5 lbs., respectively - are in excellent health, but they do need to gain some weight. He told Nice-Matin that Jolie may remain at the hospital another six or seven days while the newborns grow.

While the duration of Jolie’s hospital stay remains to be seen, Mayor Estrosi added that Pitt and Jolie have great affection for Nice and the Fondation Lenval hospital, which overlooks the Mediterranean.

“%26#91;Brad%26#93; told me we chose one of the best hospitals in the world, one of the best doctors, one of the best medical teams,” he told the paper. “And also the most beautiful bay in the world.”

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How is Angelina Jolie feeling two days after the birth of her twins? There was heightened speculation about her health Monday morning after she received a lengthy visit from her obstetrician, Dr. Michel Sussmann.

Sussmann - who delivered Jolie’s son Knox Saturday night at 6:27 p.m., followed by daughter Vivienne one minute later - left his car double parked outside the hospital for more than an hour during the early morning visit.

The obstetrician arrived at the Fondation Lenval hospital in Nice, France, around 8:50 a.m. in his black Mercedes coupe. Parked partially across a pedestrian crossing, he left the hazard lights flashing as he went inside for more than an hour.

His previous check-up visits have usually lasted around 20 minutes and the doctor normally leaves his car in the underground garage, not double-parked on the road outside.

Later, as Sussmann emerged from the hospital, he tried to allay any fears about Jolie, 33, and her newborns. “They are all very well, very well,” he told PEOPLE exclusively. “Everything is okay.”

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When the moment finally came to welcome their newborn twins into the world, Brad Pitt and Angelina Jolie were as calm as could be.

During the labor and delivery, the couple “were talking, they were together,” Dr. Michel Sussmann told reporters outside Fondation Lenval Hospital in Nice, France, where twins Vivienne Marcheline and Knox Leon were born on Saturday. “It was an epidural, so %26#91;Angelina%26#93; was awake and speaking and laughing. They were happy.”

“He was … perfectly calm, totally determined, very pleased to be at the birth of his children, very moved and very emotional,” said Sussmann.

Asked whether the birth had been a textbook delivery, Sussmann replied, “absolutely no problems.”

When will Jolie and the babies leave the hospital? “I don’t know,” he said. “She will stay for a few days. You know, in Europe it isn’t like in the United States, where the patients go home after three days. They will stay a bit longer until everything is okay.”

He added: “The babies are fine. The babies are with the mother and father and they are fine.”

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Brad Pitt was at Angelina Jolie’s side as she gave birth to a son and daughter Saturday at the Fondation Lenval hospital in Nice, France, PEOPLE has confirmed.

“The babies are doing well. The operation went just perfectly,” Dr. Michel Sussmann told PEOPLE Sunday. “Angelina is in very good spirits. Brad Pitt was at her side. He was there and all was well.”

Sussmann confirmed the Nice-Matin newspaper report that Jolie gave birth to a boy, Knox Leon, and a girl, Vivienne Marcheline, by Cesarean section on Saturday night. Knox weighed 5.03 lbs, and Vivienne 5 lbs.

The twins are the fifth and sixth children for Jolie, 33, and partner Brad Pitt, 44, who are already parents to Maddox, 6; Pax, 4; Zahara, 3; and Shiloh, 2.

The doctor told the Associated Press that the Cesarean was moved forward “for medical reasons” so that the babies could be born “in the best conditions.” He also said Jolie is expected to stay in the hospital for a few days.

On July 1, Jolie checked in to the Fondation Lenval hospital to await the births. The family has been living in the south of France since this spring.

Jolie recently told Entertainment Weekly that she was surprised - but not daunted - when she learned she was having twins. “It did shock us, and we jumped to six %26#91;children%26#93; quickly,” she said. “But we like a challenge.”

Celebrity Babies: Jennifer Lopez, Nicole Richie, Christina Aguilera and more show off their adorable additions on the cover of PEOPLE

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They’re here, officially: On Sunday, Mayor Christian Estrosi of Nice, France, presented one of the birth certificates of Angelina Jolie and Brad Pitt’s twins on the steps of Nice’s Fondation Lenval hospital, where son Knox Leon and daughter Vivienne Marcheline were born Saturday.

The typed certificate revealed that Knox was born at 6:27 p.m. on July 12. Sister Vivienne came within a minute of that time, Dr. Michel Sussmann tells PEOPLE.

The document also showed the Mayor’s signature, as well as Pitt’s initials, the letters WBP representing his full name, William Bradley Pitt.

Knox is the 3,702 registered birth certificate in Nice for 2008.

In welcoming the twins, Estrosi told reporters, “On behalf of the inhabitants of Nice, I congratulate the happy parents, the most famous couple of the world who have chosen our city for this happy event.”

Earlier in the afternoon, a large bouquet of white roses and lilies for Jolie were delivered.

Estrosi added: “I also congratulate the four brothers and sister of the newborns who are %26#91;history won’t forget it%26#93; real ‘Niçois’ (’citizens of Nice’).”

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Angelina Jolie, who is expecting twins this summer, says being pregnant makes her feel womanly and sexy.

“It makes me feel that all the things about my body are suddenly there for a reason,” she says in the July issue of Vanity Fair. “It makes you feel round and supple, and to have a little life inside you is amazing.”

Plus, the actress says that her partner, Brad Pitt, “finds pregnancy very sexy. So that makes me feel very sexy.”

The 32-year-old - already mom to Maddox, 6; Pax, 4; Zahara, 3; and Shiloh, 2, - also says she is awed by what the human body can do. When giving birth to daughter Shiloh, “I had a C-section and I found it fascinating. I didn’t find it a sacrifice and I didn’t find it a painful experience,” she tells the magazine. “I found it a fascinating miracle of what a body can do.”

As for her child-rearing philosophy, she says that as artists she and Pitt emphasize communication and play at home. “We communicate to the point where we probably annoy our children,” she says. “We have art around the house, we have books, we go to plays, we talk. Our focus is art and painting and dress-up and singing. It’s what we love.”

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Don’t expect to catch any glimpses of Angelina Jolie in her hospital room.

The hospital in Nice, France, where Jolie, 33, is staying as she awaits the birth of her twins has coated the windows of her room with special insulating material that cameras cannot see through, the Associated Press reports. The news comes after several photographs - allegedly of Jolie and Brad Pitt - have surfaced.

“It is impossible to see into Mr. Brad Pitt and Mrs. Angelina Jolie’s room,” a rep for the Fondation Lenval hospital said in a statement. “So any pictures released are either posed fakes set up by paparazzi, or, they are pictures of other patients. We hope this is clearly understood out of respect for all patients in this clinic.”

arriving at the hospital, where he visited Jolie, who is staying in a four-room suite overlooking the Mediterranean.

Pitt has been a frequent visitor, bringing the couple’s daughters, Shiloh, 2, and Zahara, 3, along. On Saturday the actress’s brother James Haven also visited.

Jolie is undergoing observation and is expected to give birth anytime “in the next weeks,” her obstetrician told reporters on July 2.

Angelina Jolie received two special visitors over the weekend in her French hospital room: brother James Haven and son Maddox.

A bodyguard carried Maddox, 6, into the hospital on Friday, July 4 to spend time with his mom, while James - wearing an orange sweatshirt and sunglasses - entered the hospital Saturday through a side entrance and stayed for an hour and a half.

Security has increased at the medical center since Jolie, 33, checked into Fondation Lenval Hospital in Nice.

During a press conference on July 2, her doctor told reporters that the actress, who is expecting twins, was not due for several weeks.