The Duchess of Cambridge and her newborn baby daughter left London's St. Mary's Hospital Saturday after a safe delivery.

Kensington Palace said the baby was born at 8:34 a.m. London time and weighed 8 pounds 3 ounces. Prince William was with his wife at the hospital along with the couple's son, Prince George. The couple and their newborn greeted the media before heading home.

The announcement was greeted by cheers outside the hospital, where die-hard royal fans dressed in patriotic Union Jack gear were camped out on the sidewalk, eagerly awaiting news. Delighted chants of "Princess! Princess!" sounded outside the hospital's private Lindo Wing.

A town crier in elaborate costume shouted out the news at the hospital's door, clanging his bell to welcome the new royal. "May our princess be long-lived, happy and glorious," said Tony Appleton, reading from a scroll in a booming voice.

The palace said Kate, 33, and her infant were doing well, and that Prince William was present for the birth.

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The princess is fourth in line to the throne and the fifth great-grandchild of Queen Elizabeth II. The statement said senior royals have been informed and "are delighted with the news."

Kate, who wed William in April 2011, gave birth to Prince George at the same hospital in July 2013.

The name of the newborn wasn't expected to be announced immediately. When George was born, officials waited two days before announcing his name.

Anticipation has been building for weeks. Kate had told a well-wisher earlier this year that the child was due in the second two weeks of April, kicking off what the tabloid press called the Great Kate Wait. The world's media had set up their positions outside the hospital for days, but were still caught slightly off guard by the speed with which officials announced the birth.

"I'm top of the world," said royal camper Terry Hutt, 80. He said he did not expect the birth to happen as soon as it did, but said: `'Babies come when they're ready."

"If Diana was here, she'd be very, very proud," he added, referring to the late Princess Diana, William's mother.

Betting had for weeks ran heavily in favor of the child being a girl, despite any apparent evidence to back that up.

All the top bets for the baby's name are for girls. Alice and Charlotte are the clear favorites, followed by Elizabeth, Victoria and Diana -- all names with strong connections to royal tradition.

Prince Charles has signaled -- twice -- that he was hoping for a granddaughter, which led some to speculate that Charles had some inside information.

Many Britons, too, say they had hoped for a princess: The monarchy has not welcomed a princess born this high up the line of succession since Princess Anne, the queen's second child, was born in 1950.

Princesses Beatrice and Eugenie, the daughters of Prince Andrew and Sarah Ferguson, were fifth and sixth in line at the time of their birth.

At 21 months, George is currently third in line to the throne, after his grandfather Prince Charles and William. The newborn becomes the fourth in line, bumping Uncle Harry to fifth place.

Thanks to a recent change in law, the princess will hold her place in the line of succession that for centuries had put men ahead of their sisters.

The Associated Press contributed to this report