Kate William with princess, Royal Baby 2 Photos

The Duke and Duchess of Cambridge emerged on the steps outside St Mary's Hospital in west London shortly after 6 pm to offer the world a brief glimpse of the new princess. Kate gave birth to a baby girl yesterday at 8:34 a.m. London time (0734 GMT), less than three hours after she was admitted.

The announcement was greeted by cheers outside the hospital, where die-hard royal fans dressed in patriotic Union Jack gear have been camping out on the sidewalk, eagerly awaiting news. A town crier in elaborate costume loudly declared the news at the hospital's door, clanging his bell to welcome the new royal.

The beaming Duke and Duchess of Cambridge left hospital Saturday carrying their newborn princess in front of hundreds of cheering well-wishers and the massed ranks of photographers from the world's media.

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The sleeping baby was wrapped in a woollen shawl as a relaxed-looking Kate, 33, cradled her in her arms in front of the private Lindo Wing of St Mary's Hospital in central London.William, 32, then drove his wife and daughter the short distance to Kensington Palace after carrying the baby out in a car seat.

Royal watchers will be keeping alert for first visits from William's father Prince Charles and his wife Camilla, and from Kate's parents, Michael and Carole Middleton.

Britain is eagerly awaiting the announcement of the new princess's name. Charlotte became the new favourite with the bookmakers on Sunday, overtaking long-time favourite Alice.

British Prime Minister David Cameron led the congratulations. "This is wonderful news and together with the whole of the country I want to give the warmest possible welcome to the new princess," he told reporters. US President Barack Obama and his wife Michelle spoke of their delight at the birth. "On behalf of the American people, we wish the duke and duchess and their son George much joy and happiness," the White House said in a statement. The new princess sits fourth in line to the throne after Queen Elizabeth's eldest son Charles, 66, his eldest son William and his eldest child George.She is the first major royal who cannot be overtaken in the line of succession by any future younger brothers following changes to the monarchy's rules to remove gender bias.

The royal couple are planning to spend the next few days at Kensington Palace. They will then travel to Anmer Hall, their secluded 10-bedroom country mansion on Queen Elizabeth's privately-owned Sandringham estate in Norfolk, eastern England.

The adorable toddler, Prince George wore colour coordinated outfits with his dad and even waved to gathered onlookers.