To William and Kate, a princess

The new baby was born at 8.34am weighing 8lbs 3oz and William was at his wife’s side during the delivery.

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 birth of the princess comes less than three months after Kate visited Portsmouth. See a report and video of her visit here.

Celebrations were in full swing outside the Lindo Wing as royal fans sang: “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 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.

David Cameron led the congratulations to the Duke and Duchess of Cambridge on the birth their new daughter.

“I’m absolutely delighted for them,” the Prime Minister declared on his Twitter feed.

Deputy Prime Minister Nick Clegg said that he and his wife Miriam wished them “all the best as their family grows”.

“This is great news and an exciting time not only for them, but also Prince George,” he said.

Scotland’s First Minister Nicola Sturgeon said she was “delighted” at the news and offered her “warmest congratulations” to the royal couple.

Labour leader Ed Miliband tweeted: “Congratulations to the Duke and Duchess on the birth of their daughter. Wishing them lots of joy and happiness - and hopefully some sleep!”

Meanwhile, Mr Clegg revealed he was invited into a voter’s house to watch the announcement on TV.

The Lib Dem leader tweeted: “On the doorstep in Sheffield. Thanks to the kind constituents who invited me in to see the great royal baby news being announced on their TV”.

Ukip leader Nigel Farage said the birth of the royal baby was an “exciting and joyous event for millions of patriotic British people”.

“I strongly urge all Ukip candidates to take at least an hour out of campaigning in order to toast the new arrival. I shall certainly be setting an example in that regard. After all, some things are worth interrupting politics for,” he said.

Mr Farage said he was happy the baby’s weight was announced in imperial measurements.

He said: “Imperial measurements, proper measurements - eight pounds three ounces.

“Not some horrid kilogramme measurement, I’m very, very pleased. Perhaps that tells us where the royal family really stand.”