Duke and Duchess of Cambridge show baby princess to the world hours after birth

William and Kate could not contain their happiness as they left hospital holding their daughter, who is fourth in line to the throne.

After waiting days outside the private maternity unit, media from across the globe and royal fans were treated to the sight of the Cambridges posing for the first time with their newborn child.

The baby - whose name has yet to be announced - was born at 8.34am weighing 8lbs 3oz, less than three hours after the couple arrived at the Lindo Wing at St Mary’s Hospital in London.

Kate cradled her daughter in her right arm and the baby, wrapped in shawl and wearing a bonnet, appeared fast asleep.

The Duchess smile broadly as did the Duke who had his arm around his wife and they both waved to the media and the crowds.

Kate looked relaxed and in good health despite giving birth only around 10 hours ago, and wore a yellow and white floral print Jenny Packham dress.

After spending a few minutes posing for pictures they walked back inside the Lindo Wing and soon returned with their daughter in a baby seat.

William carried her and the couple held hands as they walked down the Lindo Wing steps.

After the Duke placed his baby on the back seat of a Range Rover and Kate, also in a rear seat, reached over to strap her in, he drove his family away.

William had earlier brought older brother Prince George to the Lindo Wing to meet his new baby sister.

The toddler prince waved to the crowds when he first arrived with his father but he left for home before his parents, through a back entrance.

Proud father William spoke of his joy following the birth telling the waiting press he was “very happy’’ when he first left to pick up George from Kensington Palace.

Kensington Palace tweeted a close up photo of the princess and one of William, Kate and the baby on the steps of the hospital with the hashtag “# WelcomeToTheFamily”.

Some strands of dark hair could be seen around the edge of the baby princess’ bonnet which was tied under her chin during her first photocall.

The shouts from the media and the clicks of dozens of camera shutters did not seem to disturb the serene sleeping infant.

She was wearing a soft wool shawl made by the small, family-run Nottingham company GH Hurt & Son, based in Chilwell.

The firm have a long-standing connection to the Royal Family, having made the shawl that wrapped George when he first left hospital.

Kate was a number of days overdue and had been taken to the Lindo wing of St Mary’s Hospital at 6am from her nearby home Kensington Palace.

Kensington Palace said in a statement: “Her Royal Highness The Duchess of Cambridge was safely delivered of a daughter at 8.34am. The baby weighs 8lbs 3oz.

“The Duke of Cambridge was present for the birth.

“The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news.

“Her Royal Highness and her child are both doing well.”

The Duchess of Cambridge’s daughter is fourth in line to the throne, the Queen’s fifth great-grandchild and a spare to the heir - and Prince George’s sister.

The Prince of Wales will be overjoyed as he made no secret he wanted his second grandchild to be a girl.

Before the birth William and Kate said they did not know the sex of their baby, so the arrival of a daughter will be a surprise to them.

Kate’s daughter was delivered far quicker then her first child - with the baby being born less than three hours after she was admitted to hospital at 6am in the early stages of labour.

George took more than 10 hours to be born but it appears his sister might have taken less then half that time.

The Duchess is being looked after by consultant obstetrician Guy Thorpe-Beeston, who is the surgeon-gynaecologist to the household.

He was joined in the delivery room by Alan Farthing, the Queen’s surgeon-gynaecologist.

The huge numbers of journalists, photographers and broadcasters who had just assembled outside the Lindo Wing were caught a little off guard by the speed of the announcement of the birth.

A ripple of excitement went through the royal fans who had been camped outside the private maternity wing for days.

Town crier Tony Appleton - president of the Guild of International Millennium Town Criers - added a sense of drama to the occasion.

Standing on the steps of Lindo Wing and in a booming voice, he told the large crowds beginning to gather: “We welcome with humble duty the second-born of their Royal Highnesses the Duke and Duchess of Cambridge.

“The Princess is fourth in line to the throne.”

The political leaders took a moment out from General Election campaigning to congratulate the Cambridges on the birth of their daughter via Twitter.

David Cameron tweeted: “I’m absolutely delighted for them”. Labour leader Ed Miliband said: “Wishing them lots of joy and happiness - and hopefully some sleep!”.

Nick Clegg, of the Liberal Democrats, tweeted: “Miriam & I wish them all the best as their family grows.”

Scotland’s First Minister Nicola Sturgeon issued a brief statement sending the couple her “warmest congratulations”.

The official proclamation announcing the birth was erected on a golden easel at Buckingham Palace.

Crowds of tourists flocked to the palace gates as it went on display.

Hundreds of people furiously clicked at their cameras and smartphones to capture the moment.

Crowds covered the Queen Victoria memorial as they craned their necks to see the small document announcing the arrival of the fourth-in-line to the throne.

The official proclamation was put up just after the Changing of the Guard.

It had been brought from the Lindo Wing at St Mary’s Hospital where Kate gave birth to a baby girl this morning.

The Duchess of Cambridge gave birth just two hours and 34 minutes after being admitted to hospital.

The speedy announcement came after a lengthy wait for news of developments over the last week.

It appeared to be a much faster delivery than with Prince George - although Kate could have been in labour at home for several hours before she was admitted.

In 2013, she went into hospital at around 6am on the day George was born and he arrived 10-and-a-half hours later at 4.24pm, weighing 8lb 6oz.

Second and subsequent labours tend to be much faster, with active labour lasting, on average, five hours, according to parenting site BabyCentre.co.uk.

Mervi Jokinen, of the Royal College of Midwives and president of the European Midwives Association, said: “Individual labours are different, but we definitely see shorter labours second time around.

“Your body seems to be programmed. The hormones kick in quicker and progression is faster. It’s a little bit like a computer. Your body needs to be programmed first time around.

“The pushing stage can also be quicker because it’s your second one. Muscles have been stretched so you have less resistance and you have the ability to push the baby past the birth canal.”

Kate had a straightforward birth with George with no complications and, given the quick confirmation of the birth from Kensington Palace, is likely to have had the same this time.

As well as having a hospital bag packed with nappies and babygros, Kate will have made preparations for leaving the Lindo Wing in front of the world’s media.