Royal baby:
Duchess of Cambridge gives birth to daughter
The princess - who is fourth in line to the throne - was \\\"safely delivered\\\" at 08:34 BST, the palace said in a statement.
The Duke of Cambridge was present for the birth of the baby, who weighed 8lbs 3oz (3.7kg).
Both Catherine and her daughter are \\\"doing well\\\", the statement added.
The name of the baby will be announced in due course.
For live updates click here and for the royal baby special report, click here.
The Prince of Wales, who had earlier said he was hoping for a grand-daughter, and the Duchess of Cornwall said they were \\\"absolutely delighted\\\".
An official notice was placed on an easel at Buckingham Palace - it will be there for 24 hours
Police are guarding the entrance to the hospital in west London
The duchess had earlier been admitted to the private Lindo Wing at St Mary\\\'s Hospital in Paddington, where the couple\\\'s first child Prince George was born in July 2013.
The statement from Kensington Palace added: \\\"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.\\\"
The latest royal joins the line of succession behind her grandfather Prince Charles, father Prince William and brother Prince George.
The baby is the Queen\\\'s fifth great-grandchild.
Outside the Lindo Wing: Royal Correspondent Daniela Relph
Crowds began gathering after it was announced Catherine was in labour
The reporters, the camera crews, the hardy fans who\\\'ve been camping outside had settled in for a long labour. It wasn\\\'t to be.
The news came in just after 11:00 BST - the duchess had given birth to a daughter just two-and-a-half hours after arriving at hospital.
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.
The Royal Navy posted this celebratory picture by the crew of HMS Lancaster
The BT Tower in London welcomed the news
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.\\\"
Deputy Prime Minister Nick Clegg tweeted that he and his wife Miriam wished the family \\\"all the best\\\".
And Labour leader Ed Miliband wrote: \\\"Congratulations to the duke and duchess on the birth of their daughter. Wishing them lots of joy and happiness - and hopefully some sleep!\\\"
The Archbishop of Canterbury Justin Welby said: \\\"It\\\'s wonderful news that the Duke and Duchess of Cambridge have a healthy new baby girl.
\\\"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.\\\"
Some fans of the Royal Family have been outside the hospital for days
A large number of journalists, photographers and broadcasters had gathered after the announcement this morning that Catherine was in labour.
Following the announcement of the birth, standing on the steps of the Lindo Wing, unofficial town crier Tony Appleton told crowds: \\\"We welcome with humble duty the new baby of their Royal Highnesses the Duke and Duchess of Cambridge.
Duchess of Cambridge gives birth to daughter
The princess - who is fourth in line to the throne - was \\\"safely delivered\\\" at 08:34 BST, the palace said in a statement.
The Duke of Cambridge was present for the birth of the baby, who weighed 8lbs 3oz (3.7kg).
Both Catherine and her daughter are \\\"doing well\\\", the statement added.
The name of the baby will be announced in due course.
For live updates click here and for the royal baby special report, click here.
The Prince of Wales, who had earlier said he was hoping for a grand-daughter, and the Duchess of Cornwall said they were \\\"absolutely delighted\\\".
An official notice was placed on an easel at Buckingham Palace - it will be there for 24 hours
Police are guarding the entrance to the hospital in west London
The duchess had earlier been admitted to the private Lindo Wing at St Mary\\\'s Hospital in Paddington, where the couple\\\'s first child Prince George was born in July 2013.
The statement from Kensington Palace added: \\\"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.\\\"
The latest royal joins the line of succession behind her grandfather Prince Charles, father Prince William and brother Prince George.
The baby is the Queen\\\'s fifth great-grandchild.
Outside the Lindo Wing: Royal Correspondent Daniela Relph
Crowds began gathering after it was announced Catherine was in labour
The reporters, the camera crews, the hardy fans who\\\'ve been camping outside had settled in for a long labour. It wasn\\\'t to be.
The news came in just after 11:00 BST - the duchess had given birth to a daughter just two-and-a-half hours after arriving at hospital.
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.
The Royal Navy posted this celebratory picture by the crew of HMS Lancaster
The BT Tower in London welcomed the news
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.\\\"
Deputy Prime Minister Nick Clegg tweeted that he and his wife Miriam wished the family \\\"all the best\\\".
And Labour leader Ed Miliband wrote: \\\"Congratulations to the duke and duchess on the birth of their daughter. Wishing them lots of joy and happiness - and hopefully some sleep!\\\"
The Archbishop of Canterbury Justin Welby said: \\\"It\\\'s wonderful news that the Duke and Duchess of Cambridge have a healthy new baby girl.
\\\"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.\\\"
Some fans of the Royal Family have been outside the hospital for days
A large number of journalists, photographers and broadcasters had gathered after the announcement this morning that Catherine was in labour.
Following the announcement of the birth, standing on the steps of the Lindo Wing, unofficial town crier Tony Appleton told crowds: \\\"We welcome with humble duty the new baby of their Royal Highnesses the Duke and Duchess of Cambridge.
