Kate, the wife of Prince William, gave birth to a boy at a hospital in London on Monday, the third child for the British royal couple and now fifth in line to the throne.
Kensington Palace said the baby was born at 1001 GMT and weighs 8 lbs 7oz (3.9 kg). William was present for the birth at St Mary's Hospital in west London where their other two children, George and Charlotte, were also born, it 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," Kensington Palace said.
"Her Royal Highness and her child are both doing well."
The new prince is Queen Elizabeth's sixth great-grandchild and fifth-in-line to the British throne behind siblings George, 4, his two-year-old sister Charlotte, their father William, and grandfather and heir Prince Charles.
The Duchess was in early stages of labor
The Duchess of Cambridge Kate Middleton has been admitted in the early stages of labor at Lindo Wing of St Mary's Hospital, on Monday.
Kensington Palace says Prince William's wife, the Duchess of Cambridge, has entered a London hospital to give birth to the couple's third child.
The former Kate Middleton travelled by car on Monday morning to the private Lindo Wing of St. Mary's Hospital in central London.
The palace says she was in "the early stages of labor."
The gender of the baby hasn't been announced.
The couple, who married in 2011, has two other children: Prince George, four, and two-year-old Princess Charlotte.
Both were born at the same hospital, as were William and his younger brother Harry.
Line of succession to the British throne
Prince William and his wife Kate's baby will be fifth in line to inherit the British throne, behind big brother Prince George and sister Princess Charlotte.
When the baby is born, everyone below will be moved down a place, including William's brother Prince Harry who will drop from fifth to sixth position.
The immediate line of succession to the throne includes Queen Elizabeth II's four children and their descendants:
1. Prince Charles, Prince of Wales
Born 1948, eldest son of queen Elizabeth
2. Prince William, Duke of Cambridge
Born 1982, Charles’s eldest son
3. Prince George of Cambridge
Born 2013, William’s son
4. Princess Charlotte of Cambridge
Born 2015, William’s daughter
5. Baby Prince or Princess of Cambridge
Expected imminently, William’s son or daughter
6. Prince Henry of Wales (Prince Harry)
Born 1984, Charles' second son
7. Prince Andrew, Duke of York
Born 1960, queen Elizabeth’s second son
8. Princess Beatrice of York
Born 1988, Andrew’s eldest daughter
9. Princess Eugenie of York
Born 1990, Andrew’s second daughter
10. Prince Edward, Earl of Wessex
Born 1964, queen Elizabeth’s third son
11. James, Viscount Severn
Born 2007, Edward’s son
12. Lady Louise Windsor
Born 2003, Edward’s daughter
13. Princess Anne, Princess Royal
Born 1950, queen Elizabeth’s daughter
14. Peter Phillips
Born 1977, Anne’s son
15. Savannah Phillips
Born 2010, Philips' eldest daughter
16. Isla Phillips
Born 2012, Philips' second daughter
17. Zara Tindall
Born 1981, Anne’s daughter
18. Mia Tindall
Born 2014, Tindall’s daughter
Queen Elizabeth's descendants are followed by those of her late sister princess Margaret, her only sibling.
The offspring of their father king George VI's siblings then follow. There are more than 60 living people descended from his father king George V, who died in 1936.
Only people descended from Sophia of Hanover can inherit the throne, according to the 1701 Act of Settlement.
The monarchy's website goes down as far as Zara Tindall, though some counts list more than 5,700 living descendants of Sophia, including Roman Catholics, who cannot inherit.
The highest excluded person is 26-year-old Edward Windsor, Lord Downpatrick, a first cousin twice removed of the queen, who converted to Catholicism. He would otherwise be 37th in line after the new baby is born.
In changes to the succession laws which came into effect in 2015, males born after October 28, 2011, no longer take precedence over their older sisters.
Also people married to Catholics are no longer excluded, with Downpatrick's father George Windsor, the Earl of St Andrews, the highest person restored to the line.
The line is a vast tangle of nobility and ordinary, untitled descendants from all corners of Europe. Several other European monarchs feature.
Besides Britain, it is also the line of succession to the thrones of 15 other Commonwealth realms.