Britain's Prince William, Duke of Cambridge, and his wife Catherine, Duchess of Cambridge show their newly-born daughter, their second child, to the media. Photo / Getty Images
The Duke and Duchess of Cambridge have arrived home with their new baby daughter just hours after she was born this morning.
The couple emerged on the steps outside the Lindo Wing at St Mary's Hospital and the world was given a brief glimpse of the new princess, who was wrapped in a white blanket.
The newest royal, who is name is not yet known, was born at 8.34am on Saturday UK times weighing 8lbs and 3oz - less than three hours after the Duchess was admitted to hospital.
She was soundly asleep when her parents presented her to the cameras and the crowds of well-wishers camped outside the hospital.
Prince William and Kate smiled and waved as they posed for pictures with their new baby then briefly returned to the hospital.
They then emerged again, with Prince William carrying his sleeping baby in a car seat. He loaded her into the back of a people carrier before they all drove off to Kensington Palace.
The royal couple and their new addition will remain at Kensington Palace for a few days, before moving to their new home in Norfolk to rest.
The country estate at Anmer Hall is a stone's throw away from the Queen's country retreat of Sandringham.It is believed the young family will split their time between Anmer Hall and Kensington Palace as they take time out to be with their new arrival.
Prince William is understood to be taking a few weeks off to be with his wife and two children.
In a statement posted on the royal Twitter account, the couple said: "Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have all received.
"They would also like to thank everyone for their warm wishes."
Earlier in the day, Prince William took Prince George to the Lindo Wing to meet his newborn sister. The 21-month-old almost stole the show when he gave a timid wave to the crowds from the hospital steps.
Cheers erupted for the young prince, who has not made a public appearance in the UK since his own birth in 2013, as he made his way towards the Lindo Wing in his father's arms.
He was driven from the family home at Kensington Palace to St Mary's Hospital by his father, Prince William, and stayed for about an hour before he was taken back home for his bath and tea with his nanny.
When they arrived, William carefully took George out from his safety seat in the back of the Range Rover and could be seen whispering a few reassuring words.
He attempted to put the toddler down but George, dressed in a blue jumper, shorts and socks, was having nothing of it and William picked him up again.
There was, however, a half smile for the cameras and a little wave over his father's shoulder as they walked inside. William also tenderly kissed his first born son on the head.
William had beamed with pride as he left hospital to pick up George. Before getting into his black Range Rover, he said: "we're very, very happy."
Both Kate and her newborn daughter were said to have been "doing well" when the news of the birth was announced. The baby, whose name is not yet known, will be known as Her Royal Highness Princess of Cambridge.
The announcement came by way of a statement released by Kensington Palace shortly after 11am UK time. It was then posted on the palace's official Twitter page two minutes later.
Her Royal Highness The Duchess of Cambridge was safely delivered of a daughter at 8.34am.
— The Duke and Duchess of Cambridge (@KensingtonRoyal) May 2, 2015
"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 new princess is fourth in line to the throne.
Prime Minister John Key sent a message of congratulations to Kate and William on behalf of New Zealand.
"On behalf of the people of New Zealand I would like to congratulate Prince William, Catherine and Prince George on this wonderful news.
"This is a very special time for any family. The Duke and Duchess are excellent parents and I am sure Prince George will adore his new little sister."
New Zealand's official gift to the Royal couple will be a selection of woollen baby items from Hutt Valley company, Stansborough, including a pelt teddy bear.
"I wish Prince William, Catherine, Prince George and the Royal Family all the very best," says Mr Key.
In Auckland, the Sky Tower turned pink to mark the occasion.
To mark the birth of the princess, soldiers of the 16 Field Regiment Royal New Zealand Artillery will fire a 21-gun salute at Point Jerningham, Wellington, at 12pm tomorrow.
The Saluting Battery, the only permanent battery authorised to perform artillery salutes, comprises four modified 25-pounder guns and will fire blank rounds.
A new coin is being minted in New Zealand to commemorate the birth of the royal princess. The design has been approved by Buckingham Palace.
British Prime Minister David Cameron and UK Opposition Leader Ed Miliband also sent their best wishes to the couple on Twitter:
PM: Congratulations to the Duke and Duchess of Cambridge on the birth of their baby girl. I'm absolutely delighted for them.
— UK Prime Minister (@10DowningStreet) May 2, 2015
Congratulations to the Duke and Duchess on the birth of their daughter. Wishing them lots of joy and happiness - and hopefully some sleep!
Celebrations were in full swing outside the Lindo Wing with royal fans singing: "Princess! Princess! Princess!"
After several days of camping outside, dedicated royalists were singing and dancing with joy at the news that the Duchess of Cambridge has given birth to a baby girl.
Terry Hutt, who celebrated his 80th birthday this week and is from Weston-super-Mare, said: "I'm on top of the world."
He said he did not expect the birth to happen as soon as it did, but said: "Babies come when they're ready."
Mr Hutt added: "If Diana was here, she'd be very, very proud."
The BBC reported that Twitter recorded 4500 tweets a minute with the hashtag #royalbaby at 11.25am UK time - the peak time for the story on social media.
Royal change of the rules
Although the new princess is unlikely to ever become queen, it is not unheard of for a second child in the direct line of succession to accede to the throne.
Mostly recently the Queen's own father, King George VI, replaced his elder brother, King Edward VIII, who abdicated over his love for the "unsuitable" American divorcee Wallis Simpson.
Thanks to a recent change in the law, the couple's daughter cannot be superseded in her claim to the throne by any younger brother who may yet come along.
The Succession to the Crown Act, passed in 2013, means that male heirs no longer precede their elder sisters in the line of succession
A 2012 intervention by the Queen also means that the new baby will automatically become an HRH - Her Royal Highness - and be permitted to take the title of princess.
As the second child of the second heir to the throne she would, until then, only have been a Lady.
Image 1 of 10: Catherine, Duchess of Cambridge and Prince William, Duke of Cambridge at the Lindo Wing with their newborn daughter at St Mary's Hospital. Photo / Getty Images
Her arrival will shunt his uncle, Prince Harry, down to fifth in the order of succession. Her great uncle, Prince Andrew, will fall out of the top five for the first time to sixth.
Many royal watchers had been desperately hoping for a girl - the last to be born in the direct line of succession was Princess Anne back in 1950.
Both Prince Charles and William's late mother, Diana, Princess of Wales, both openly longed for a girl to add to their family.
Indeed when congratulated by a member of the public about the news that he would become a grandfather again last year, he said candidly: "It's wonderful to be a grandfather again. I'm looking forward to it. But I hope it will be a girl this time."
Kate herself has said William was hoping for a daughter, although his brother, Prince Harry, joked William probably doesn't realise what he was taking on.
News of her birth came in the form of a press release to media organisations followed by a formal - and very modern - announcement two minutes later on the palace social media channels.
However, it was made public only after the Queen and other family members had been informed, including Prince Charles, now a grandfather twice over, the baby's uncle Prince Harry, who is currently on an army detachment in Australia, and, of course, Kate's parents, Michael and Carole Middleton, who will play a dominant part in their new grandchild's life.
A week overdue
Kate was driven from her apartment at Kensington Palace to St Mary's Hospital in Paddington, west London, accompanied by her husband, Prince William, earlier today.
The couple's nanny, Maria Borrallo, is looking after their eldest son, Prince George, who turns two in July.
The Duchess was around a week overdue and the had been much speculation all week that she may have to be induced.
Kate's medical team at the Lindo, which charges £12,000 for a natural delivery even without complications, was led by the hugely experienced Guy-Beeston, Surgeon-Gynecologist to the Royal Household.
When Kate gave birth to her eldest child in 2013 she was admitted to the Lindo Wing at 5.30am and delivered her son, George, at 4.24pm the same day, although the birth wasn't officially announced for several hours as the couple wanted time to bond with their child.
Bookies have strongly favoured the baby being a girl, with favourite names including Alice, Elizabeth, Charlotte and Victoria. If it's a boy top choices include James, Arthur, Louis and Philip.
William and Kate announced they were expecting their second child on September 8, 2014, in an announcement made early because she was forced to cancel an official engagement because she was suffering from the same severe morning sickness she had with Prince George.
On October 20, 2014, following their 12-week scan, they announced they were expecting their baby in April.
Kate's pregnancy style second time around
The Duchess of Cambridge refused to let her style icon status slip during her second pregnancy. Rather than swaddling her growing bump under baggy dresses, the 33-year-old dressed to impress every time she stepped out.
But while Mulberry coats and Alexander McQueen gowns did creep in, much of Kate's pregnancy wardrobe came from the High Street.
Check out all of Kate's looks during her second pregnancy here:
Image 1 of 29: The Duke and Duchess attend the ceremonial welcome for Singapore's President Tony Tan Keng Yam at the Royal Garden Hotel on October 21, 2014 in London, England. Photo / Getty Images
How it unfolded last time
With the new princess born, we look back at the major milestones the Duke and Duchess faced the first time Kate was pregnant, with Prince George.