THE wait was finally over.

After weeks of anticipation and feverish speculation after the Duchess of Cambridge told a well-wisher she was due around late April, at 8.34am on Saturday a new royal princess entered the world.

Weighing in at eight pounds and three ounces the infant and her family received congratulatory messages from around the world.

The Duke and Duchess of Cambridge, who marked their fourth wedding anniversary just two days previously, arrived at St Mary's Hospital at 6am on Saturday and just two hours later the baby girl was born.

The birth was greeted with cheers and ecstatic cries of "Hip, hip, hooray" and "Princess! Princess" outside the palace and outside the hospital where royal fans and the worlds' media had been camped for days.

William announced he was "very happy" as he brought George to the hospital to meet his baby sister. George, looking perplexed by all the cameras, waved at the crowds.

The couple emerged later the same day with the baby wrapped in an ivory woollen shawl and bonnet to pose for photographs on the steps of the hospital, a little over 12 hours after Kate arrived.

Kate, wearing a yellow-and-white floral shift dress by British designer Jenny Packham - cradled the sleeping princess wrapped in a white shawl in her arms.

A few minutes later, Prince William carried the baby in a car seat to a waiting vehicle, and then drove his wife and new daughter the short distance to Kensington Palace.

The baby princess will be fourth in line to the throne behind her brother Prince George, father William and grandfather Prince Charles, pushing her uncle Prince Harry down a place in the royal hierarchy.

The announcement of the birth was a mix of the traditional and modern. An official notice was placed at Buckingham Palace - an age-old custom - and town crier Tony Appleton stood on the steps on the Lindo wing to announce the news.

However a series of tweets from the official Kensington Palace account also announced the safe arrival of the baby girl, her weight and that "Her Royal Highness and the child are both doing well."

One fan who had camped out outside the hospital for days danced with joy.

"I'm top of the world," said royal camper Terry Hutt, 80, decked out in patriotic Union Jack gear. 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.

The Queen and senior royals were "delighted with the news," officials said.

The Queen marked the arrival of her fifth great-grandchild occasion by wearing a pink ensemble while carrying out an official engagement in North Yorkshire.

Britain's leading politicians took time out from the election trail to send their best wishes.

Prime Minister David Cameron tweeted: "Congratulations to the Duke and Duchess of Cambridge on the birth of their baby girl. I'm absolutely delighted for them," while Labour leader Ed Miliband said the news was fantastic and added "I know the whole country will be wishing them well."

First Minister Nicola Sturgeon said: "I am delighted at the news of the birth of Prince William and Catherine's daughter, and I send them my warmest congratulations.

"I'm sure people across Scotland join me in sending their very best wishes to the proud parents, and to big brother George."

The Moderator of the General Assembly of the Church of Scotland, Rt Rev John Chalmers, who is also a Chaplain to the Queen in Scotland said, "It is always a joy to welcome the safe arrival of a child. I'm sure that I speak for members of the Church of Scotland when I wish the Earl and Countess of Strathearn, their daughter and Prince George all the happiness in the world.

"They can be assured of our prayers and best wishes."

President Barack Obama said he wished the family "much joy and happiness," while Canadian Prime Minister Steven Harper said the British royal family held a "very special place in our country.

She may have been little over a day old but the new princess was already proving more popular than her older sibling Prince George - at least online.

Twitter stats show that more than a million tweets for the new royal baby on Saturday while her brother's birth in 2013 attracted 900,000 posts.

And there was immediate speculation over whether the as yet unnamed princess would be getting a Scottish title.

Kate and William met at a Scottish university and have their own separate titles in Scotland, where they're known as the Earl and Countess of Strathearn - the title used by First Minister Alex Salmond when he congratulated the couple on news of the pregnancy.

She may not be a royal but Carole Middleton was one of the first people to meet the new princess even before Prince Charles.

Dressed in a white patterned blouse, the proud grandmother drive into Kensington Palace at around 11.30am on Sunday morning in a black Range Rover with her daughter, Pippa Middleton, 31.

The doting grandmother is understood to have played a key role in supporting her daughter during both her pregnancies and with childcare duties.

An hour and a half later, Prince Charles, 66, arrived at the palace with Camilla, Duchess of Cornwall, 67, to meet his granddaughter for the first time driving a light green Audi. They later drove out of the palace at 2.25pm waving to the crowd, after spending an hour and a half at the palace.

Meanwhile Kate and William's official Twitter feed - @KensingtonRoyal - invited members of the public to post images of their newborns online under the hashtag #WelcomeToTheFamily.

Messages came from as far away as Australia, as well as some parents closer to home.

One excited British mother currently living in Hong Kong posted a picture of her little boy born yesterday, adding her congratulations to all newborns and their parents.

Rhian Addiscott in Wales posted a picture of her newborn, while little Leah Lauffer from Scotland's birth was proudly announced, having arrived around eight hours ahead of the new princess.

The Royal Mint revealed the design of a new commemorative £5 coin to mark the princess's arrival.

A range of official commemorative china celebrating the birth of the princess was also unveiled.

The Royal Collection Trust designs - in white and gold - feature a playful carousel of lions and unicorns from the Royal Arms dancing among golden stars, surrounded by swaying garlands, tassels, ribbons and bows.

They also include the Duke and Duchess of Cambridge's coronet, and a pattern of oak leaves from the Middleton family's coat of arms.

Most of the pieces bear the words "Celebrating Our New Royal Baby" as well as "2015" and "Buckingham Palace".

When George was born in 2013, his official china was blue, white and gold, but the designs this time feature white and gold, rather than the traditional pink for a girl.

Babies born on the same day as the princess are eligible to receive one of 2,015 free ''lucky'' silver pennies from the Royal Mint.

The first silver penny was presented to new parents Chantal and Miguel Abel whose daughter Sofia arrived at the Chelsea & Westminster Hospital in London at 11.30am on Saturday - around three hours after the royal birth.

The royal birth appeared in the weekend Court Circular - the official record of royal engagements.

The notice reads: "KENSINGTON PALACE - 2nd May, 2015 - The Duchess of Cambridge was safely delivered of a daughter at 8.34 a.m. today. Her Royal Highness and her child are both well. Signed: Guy Thorpe-Beeston, Alan Farthing, Sunit Godambe and Huw Thomas."