The Duke and Duchess of Cambridge have left St Mary's hospital after the duchess gave birth to a daughter, the first Princess of Cambridge to be born for more than 180 years.
Earlier
Prince William has left the Lindo Wing, driving himself to Kensington Palace a few minutes ago. He said "we're very,very happy," adding: "I'm just going to pick up George."
A few minutes later
Prince George, as ever, has stolen the show, for now at least. On his first "official" appearance in front of the public in Britain since the day after his birth, he waved obediently at his father's command, though his first smile in public is yet to come.
George toddled a few steps after William put him down on the pavement, then reached up to be picked up, and, wearing all blue like his father, waved to the gathering, screaming crowd across the road before posing on the steps and waving again, for which he earned a quick kiss from his father.
Prince William's wife Kate has given birth to a baby girl. The baby, weighing 8lbs, 3oz, was born at 8.34am UK time.
The announcement was made on Kensington Palace's Twitter page. Later on, an official announcement was placed on an easel at Buckingham Palace.
It said Prince William was present for the birth of his second child. The Queen has been informed of the good news.
The Duchess was admitted early Saturday to a London hospital for the birth of the couple's second child. THe girl will be fourth in line to the throne and the fifth great-grandchild of Queen Elizabeth II.
In a brief statement, palace officials said the Duchess of Cambridge was admitted at 6 a.m. local time (0500 GMT) Saturday at St. Mary's Hospital. She traveled by car to the Lindo wing with William.
The baby is a younger sister to William and Kate's first child, Prince George, who was born July 22, 2013 at the same hospital.
Anticipation has been building for days. Kate had told a well-wisher earlier this year that the child was due in the second two weeks of April, kicking off what the tabloid press called the Great Kate Wait.
Die-hard royal fans have camped outside the hospital for days. Several keen fans, draped in Union Jack flags and waving festive banners, waited patiently on the sidewalk, hoping for a glimpse of the family.
William, who is on leave from his job as an air ambulance pilot, had been expected to be at his wife's side in the hospital, as he was for George's birth.
The couple has said that they don't know whether the baby will be a boy or a girl.
That's been a boon for Britain's bookmakers, who say they have received thousands of bets on the newborn's gender and possible name.
Most people seem convinced that it will be a girl, despite the lack of any solid evidence to back that up.
All the top bets for the baby's name are for girls - Alice and Charlotte are the clear favorites, followed by Elizabeth, Victoria and Diana. All of the names have strong connections to royal tradition.
Prince Charles has signaled - twice - that he's hoping for a granddaughter, which led some to speculate that Charles has some inside information.
But many probably just hope Britain will see a new princess: The monarchy has not welcomed a princess born this high up the line of succession for many years.
Princess Anne, Charles' sister, was born third in line in 1950. Princesses Beatrice and Eugenie, the daughters of Prince Andrew and Sarah Ferguson, were fifth and sixth in line at the time of their birth.
Update
Ladbrokes have now suspended betting on all Royal baby bets except the name, (lest someone at the hospital manages to put a stack of cash on the sex of the baby after it's already been born, presumably).
Ladbrokes' Jessica Bridge, who will be as relieved as anyone that the baby is finally coming. said: "As soon as the nation's awake baby betting is going to go berserk. Punters have been well in favour of a girl over the last 9 months, and it would be a huge surprise to them if George is joined by a little brother soon."
Here are the latest odds on the name:
Alice 6/4
Charlotte 3/1
Elizabeth 6/1
Victoria 10/1
James 14/1
Diana 14/1
Alexandra 16/1
Arthur 16/1
Henry 25/1
Catherine 25/1
Phillip 25/1
William 25/1
Frances 25/1
Mary 25/1
Albert 25/1
Alexander 25/1
Update 2
Assuming the baby is born today, it will share its birthday with David Beckham (40) and Englebert Humperdinck.
Prince William is good friends with Becks, so he will no doubt have a private joke with him about how he upstaged the big Beckham bash next time they meet. 
Update 3
David Cameron, no doubt hoping for a baby bounce in the polls as the feel-good factor kicks in, has been on BBC Breakfast giving his thoughts. "One of the privileges of my job is you get to see them up front and they are a wonderful couple, they are loving parents.
"With the rest of the nation I'll be wishing them well today, hoping for a healthy and happy outcome."
"I know St Mary's Paddington quite well, my son Ivan spent a lot of time there, so I can write a guidebook about all the local pubs and restaurants - but I'm not sure they'll have a lot of time for that - but wishing them well and hoping for a happy outcome today."
Reactions
The Senior Service has sent a congratulatory message to The Duke and Duchess of Cambridge on the birth of their new daughter.
Sailors standing on the flight decks of Type 23 frigate HMS Lancaster spelt out the word SISTER.
HMS Lancaster, known as the 'Queen's Frigate' sent their message of congratulations to her Her Majesty The Queen on the birth of her youngest great-grandchild.
And that of the President of Malta
