Postpublished at 13:42 British Summer Time 2 May 2015
BBC journalist Henrietta McMicking
tweets, external: The pink bunting is already up at St Mary's Paddington #royalbaby
Summary
The Duke and Duchess of Cambridge have left hospital with their new baby daughter, who slept throughout
The new princess was born at 08:34 BST (07:34 GMT), on 2 May, 2015, two-and-a-half hours after the Duchess of Cambridge was admitted to hospital
Prince William told reporters he was "very happy" at the arrival of his second child
The duke brought Prince George to the hospital so that the young prince could meet his sister
The name of the baby, fourth in line to the throne, is yet to be announced
Postpublished at 13:42 British Summer Time 2 May 2015
Breaking Newspublished at 13:40 British Summer Time 2 May 2015
The Prince of Wales and the Duchess of Cornwall are "absolutely delighted" at the birth of the baby princess, Clarence House has said.
Get involvedpublished at 13:38 British Summer Time 2 May 2015
Boris Johnson, Mayor of London
@MayorofLondon tweets, external: Huge congratulations to the Duke & Duchess of Cambridge on the birth of their baby girl. I know Londoners will join me in wishing them well.
Alice or Charlotte?published at 13:38 British Summer Time 2 May 2015
Lots of bets have been placed on the news baby princess' name. Alice - which has long-running royal links and was the name of the Duke of Edinburgh's mother - remains the clear favourite with Coral, which offers odds of 5/4, and Ladbrokes, which gives odds of 7/4. However, Paddy Power has Charlotte as favourite at 5/2.
Picturespublished at 13:33 British Summer Time 2 May 2015
Image source, PAClick here for all the best photographs from outside the Lindo Wing and from Buckingham Palace.
A baby bullpublished at 13:31 British Summer Time 2 May 2015
The new princess has something in common with her great-grandmother, the Queen - they are both Taureans.
Astrologer Patrick Arundell says a Taurean royal would take their official duties very seriously. He adds: "They would realise that this is something you have to do and take it more in their stride and be patient. Taurean people are very, very dependable but they can be a little bit frustratingly stuck in their ways."
It's those doors againpublished at 13:26 British Summer Time 2 May 2015
Image source, ReutersBBC's Daniela Relph, who was outside the Lindo Wing at St Mary's Hospital, described the moment news of the birth was announced.
She said: "As news filtered through outside St Mary's there were cries and cheers and an official town crier made his own birth announcement.
"It's now a mass of media, police, royal fans and curious passers-by. The wait now begins again - will the duke and duchess and their new princess leave hospital today? All eyes are on the Lindo Wing door."
Get involvedpublished at 13:25 British Summer Time 2 May 2015
Official British Airways Twitter account
@British_Airways tweets, external: She's here! Congratulations to The Duke and Duchess of Cambridge on their healthy baby girl. #RoyalBaby
Postpublished at 13:23 British Summer Time 2 May 2015
The Archbishop of Canterbury, Justin Welby, has said it is "wonderful news that the Duke and Duchess of Cambridge have a healthy new baby girl". He said: "Like many here and abroad, I'm delighted for the royal couple on this special day. May God bless them and both of their children with love, health and joy."
Postpublished at 13:13 British Summer Time 2 May 2015
The prospect of a new girl in the family will obviously please the Prince of Wales, a father of two sons.
Just yesterday, when he was presenting new colours to the 1st battalion Welsh Guards, he told 100-year-old Eric Jones: "We're hoping for a granddaughter".
Postpublished at 13:07 British Summer Time 2 May 2015
It may be a little while before the new princess gets to meet her paternal uncle. Prince Harry is currently in Australia for a four-week placement with the Australian Defence Force. Despite the time difference, he has been kept in touch with developments from the Lindo Wing.
'Get a grip'published at 13:01 British Summer Time 2 May 2015
Meanwhile, Republic - which campaigns for a democratic alternative to the monarchy - has called for the media to "get a grip" over the royal baby. Republic's Graham Smith said, external: "This may be news, but it's not big news, it's not headline news and it's not news most people are interested in beyond brief curiosity."
Tower messagepublished at 12:58 British Summer Time 2 May 2015
London's BT Tower has also sent its own message of congratulations to the duke and duchess.
Get involvedpublished at 12:53 British Summer Time 2 May 2015
Michelle Goddard from Doncaster emails: "Ingrid Seward who is commenting along with Charles Anson was speculating about the new addition's future career; 'She obviously won't be joining the Armed Forces'. Why can't the new Princess join up? They are a modern Royal Family. William and Harry did."
Twitter peakpublished at 12:53 British Summer Time 2 May 2015
BBC royal correspondent Peter Hunt says Twitter recorded 4,500 tweets a minute with a royal baby hashtag at 11:25 BST - the peak time for the story on social media.
Better than Twitter?published at 12:47 British Summer Time 2 May 2015
Forget your Twitter and suchlike. The notice on the easel has been the traditional way of announcing a royal birth for as as long as Buckingham Palace has been the Sovereign's official residence (from 1837).
The bulletin will be on display for approximately 24 hours. After it comes down, it is sent to the Privy Council Office in order that the details of the official notice may be recorded in the Privy Council records.
Large crowdspublished at 12:44 British Summer Time 2 May 2015
Hundreds of people furiously clicked cameras and smartphones to capture the moment the golden easel was placed outside Buckingham Palace, with crowds covering the Queen Victoria memorial.
Not a Maggie?published at 12:42 British Summer Time 2 May 2015
Asked by the BBC's Peter Hunt whether he had any suggestions for a name - possibly Maggie or Margaret - Labour leader Ed Miliband said "the last thing they need, certainly from politicians is advice on names", adding: "I'm sure they'll make the right judgement on that."
Get involvedpublished at 12:39 British Summer Time 2 May 2015
James Brooks, Chief Reporter for @RoyalCentral in London
@james_elliott_ tweets:, external Paddington, LondonProsecco for the press! Always welcomed! @Coral are out celebrating the birth of #PrincessCambridge.
Postpublished at 12:37 British Summer Time 2 May 2015
Image source, EPAThe princess is the Queen's fifth great-grandchild. The others are George, Savannah, Isla and Mia.