Prince William will be leaving St Mary's Hospital at around 16:00 BST to visit his son, Prince George, at Kensington Palace, the palace has said.

Amid frenzied speculation about the name of the new princess. Historian and royal author Hugo Vickers says the new baby may one day be known as the Princess Royal. The honorary title, which is currently held by Princess Anne, is customarily given by the sovereign to his or her eldest daughter.

Dickie Arbiter, Royal Commentator

@RoyalDickie tweets, external: It's buzzing @Lindowing.The big question is will William & Catherine take their new Princess home today?

BBC royal correspondent Sarah Campbell has written about royal siblings - and their potential pitfalls.

"Royal siblings have had tricky relationships over the years. One of the most dramatic falling outs came in 1478, when Edward IV reportedly had his younger brother George, Duke of Clarence - suspected of treason - drowned in a butt of wine," she said.

Click here to read her full piece.

Mayor of London Boris Johnson has been speculating on the name of the baby. He told BBC Radio Oxford: "I suggested to a certain amount of apathy that she should be called Victoria in honour of the coming Conservative victory.... What will she be called? Who knows? Coalitia? Let's hope not."

Victoria Arbiter, Royal Commentator for CNN, CBS, Entertainment Tonight

@victoriaarbiter tweets, external: The royal family's latest edition is the first Princess of Cambridge to be born in 182 years! #RoyalBabyGirl

Do you fancy following in royal footsteps by having your baby born at the Lindo Wing? A suite at the private wing costs £6,570 for a one-night stay with "normal delivery". But the costs mount up if it's a Caesarean section. But WiFi is available - if that helps make your mind up

Image source, Getty Images

We've still not had word about whether the royal couple will leave the hospital with their baby daughter today - but if they do leave this is the bank of press photographers that awaits them.

Chancellor of the Exchequer George Osborne has also reacted to the royal news, saying: "I'm really happy for the young couple. Great they've had a baby girl. And I think the whole country will be thrilled that politics won't be on the front page of the Sunday newspapers tomorrow."

Betting fever has intensified since news of the birth broke, with William Hill saying it has taken more than £55,000 in new bets in the first three hours since it was announced. William Hill spokesman Rupert Adams said: "Alice and Charlotte are still the favourites, but keep an eye out for Rose and Grace."

Wondering how the news was announced in Pakistan? This is what Samaa TV told their viewers: "The British royal family has expanded. A little fairy has become a part of it. Kate Middleton has given birth to a girl. When she grows up, we will know whose face and eyes she resembles, whether her hair is as lovely as her mother's. The visuals you are now seeing are from outside the hospital. And we tell you, in the British Royal Family, has arrived a tiny, new guest."

Image source, PA

Nice anecdote from Deputy Prime Minister Nick Clegg who said he got the news of the royal birth after he had been asked into a family home while canvassing and glimpsed at their TV. He said: "I walked into their hallway and we were talking and then suddenly I saw the television was on in the background in the sitting room, and I saw the news flash up that a new royal baby has been born this morning."

Kay Burley, Sky News journalist

@KayBurley tweets, external: Will we see new royal princess today #RoyalBaby

Wondering where the baby princess stands in the Royal Family tree? See our story on the succession line here.

Image source, PA

The list of famous people the baby princess shares her birthday with is long and quite impressive. The list includes; ex-England footballer David Beckham, singers Lily Allen and Engelbert Humperdinck, fashion designer Donatella Versace, cricketer Brian Lara, Poirot star David Suchet, as well as horticulturist Alan Titchmarch, inventor Sir James Dyson and snooker star Jimmy White.

The Royal Mail has said it will commemorate the princess's birth with a special postmark on letters delivered on Tuesday, reading: "Congratulations TRH The Duke and Duchess of Cambridge on the birth of their daughter."

It is the first time in Royal Mail's 500-year history that a royal birth has been commemorated in this way.

Julie Lischer has been celebrating the news of the royal birth in Marietta, Georgia, USA: "I turned on the computer and saw the news. It was wonderful! We held a shower for the royal baby. I served scones and cucumber sandwiches and all kinds of royal treats. I invited my friends. Everyone came in their finery and hats."

Image source, Julie Lischer

The Duke of Cambridge's uncle, Earl Spencer - brother of the late Diana, Princess of Wales - has said the birth of the princess was "wonderful news", saying: "We are all thrilled for all four of them."

@OK_Magazine tweets:, external Kate Middleton's hairdresser has ARRIVED at the Lindo Wing. #RoyalBaby

@TowerBridge tweets:, external Congratulations to the Duke & Duchess of Cambridge on the birth of a baby girl! Tonight we'll turn pink to celebrate.