The Duchess of Cambridge has given birth to a son, Kensington Palace said tonight.
The baby weighed 8lbs 6oz and was born at 4.24pm, the palace said.
A Buckingham Palace spokesman said: "The Queen and Duke of Edinburgh are delighted at the news.''
Kensington Palace said in a press release: "Her Royal Highness The Duchess of Cambridge was safely delivered of a son at 4.24pm.
"The baby weighs 8lbs 6oz.
"The Duke of Cambridge was present for the birth.
"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.
"Her Royal Highness and her child are both doing well and will remain in hospital overnight.’’
Soon after the palace announcement was made, a notice giving details about the baby - the third-in-line to the throne - left St Mary's Hospital in London by car for Buckingham Palace.
It has been signed by the Queen's former gynaecologist Marcus Setchell, who led the medical team that delivered Kate's baby.
The notice will be placed on an easel in the palace's forecourt just like the announcement of William's birth on June 21, 1982, a traditional element of theatre in marked contrast to the modern age of emails and Twitter.
The new royal baby will be the Queen's third great-grandchild and is destined to be crowned monarch.
He will be the 43rd sovereign since William the Conqueror if, as expected, it follows reigns by the Prince of Wales then William.
The new royal baby is third in line to the throne and a future king.
A great-grandchild to the Queen - her third - the newborn will also one day be crowned sovereign.
If the baby follows after the Prince of Wales and the Duke of Cambridge as king, he will be the 43rd monarch since William the Conqueror obtained the crown of England.
The baby's uncle, Prince Harry, now moves to fourth in line to the throne, while the Duke of York shifts down to fifth and Princesses Beatrice and Eugenie to sixth and seventh place.
The last time a still-serving monarch got to meet a great-grandchild born in direct succession to the crown was nearly 120 years ago.
Queen Victoria, who reigned until 1901, was still sovereign when her great-grandchild Edward VIII, who later abdicated, was born third in line in 1894.
His brother George VI was also born in Queen Victoria's lifetime, arriving fourth in line in 1895.
The last great granddaughter of a still-serving sovereign born in direct succession on the male line was their sister Princess Mary in 1897.
William and Kate's baby is the great-great-great-great-great-grandchild of Queen Victoria.
The Queen has already welcomed her first great grandchild, Savannah Phillips - daughter of Peter and Autumn Phillips - but Miss Phillips was born only 12th in line down the female line as a granddaughter to the Princess Royal and is now in 13th place.
Her second great-grandchild - Savannah's sister Isla - was born in March last year. Her fourth great-grandchild - Zara Phillips and Mike Tindall's baby - is due in the new year.
William and Kate's baby will one day be head of the armed forces and the Church of England, and possibly head of the Commonwealth, if the role is maintained in the future.
The baby is also a first grandchild for heir to the throne Charles, although he has had plenty of practice in the role as his wife, the Duchess of Cornwall, already has five grandchildren. The baby will be a first grandchild for Kate's parents Michael and Carole Middleton.
The new royal baby is the first Prince of Cambridge to be born for more than 190 years.
The last was Prince George of Cambridge, a grandson of George III and the only son of Prince Adolphus Frederick, the 1st Duke of Cambridge.
Prince George of Cambridge was born in 1819 and refused to have an arranged marriage. He wed a commoner for love after falling for the actress Sarah Louisa Fairbrother, who was said to be a classic beauty and a graceful dancer.
They married in 1847 when she was already the mother of two of his children and pregnant with his third.
But the Duke did not seek the sovereign's approval and the marriage was never recognised, hence his children were not eligible to inherit royal titles.
Miss Fairbrother was ostracised by the Royal Family and never given a title. Instead she became known by the nickname Mrs FitzGeorge and this surname was taken by George's offspring.
Despite his marriage, George had a wandering eye and soon after he wed he took up with mistress Louisa Beauclerk, who remained his lover for more than 30 years.
He went on to become the 2nd Duke of Cambridge after his father's death.
The Duke was in the Army and served in the Crimean War. He was promoted to Commander-in-Chief in 1887 and an equestrian statue of him stands in the middle of London's Whitehall.
He was said to have been a disciplinarian, who believed Army promotions should be based on social connections rather than ability. He died in 1904.
His father, the 1st Duke of Cambridge - who lived from 1774 to 1850 - was never a Prince of Cambridge, but was given the title the Duke of Cambridge by his father George III in 1801 when he was 27.
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