Kate, the wife of Prince William, gave birth to a baby boy on Monday, the couple's third child who is fifth in line to the British throne.
The boy, weighing eight pounds and seven ounces (3.8 kilogrammes), was born at 11:01 am (10:01 GMT), Kensington Palace announced.
Mother and baby are both doing well, the palace said, and William, the Duke of Cambridge, was present for the birth.
William was seen smiling as he left St. Mary's Hospital in central London shortly after 4:00 pm, waving to media outlets from around the world assembled outside.
He returned half an hour later, having collected from school the couple's two other children; four-year-old Prince George and Princess Charlotte, aged two.
Charlotte gave a wave to the crowd of onlookers and media as the trio entered the hospital,
Queen Elizabeth II, William's father Prince Charles, and his brother Prince Harry were said to be delighted with the news.
"Her Royal Highness The Duchess of Cambridge was safely delivered of a son at 11:01 hours," the palace announced in its brief statement.
Prime Minister Theresa May led the messages of support saying: "My warmest congratulations to the Duke and Duchess of Cambridge on the birth of their baby boy.
"I wish them great happiness for the future."
Kate, 36, was admitted early Monday to the hospital's private Lindo Wing, where she had given birth to George and Charlotte.
Royal fanatics, who had been camped outside the hospital wing for several days in anticipation, jumped for joy and popped open champagne.
"We're going to celebrate with fish and chips!" said John Loughrey, who was wearing a Union Jack hat and clutching a plastic doll with a crown.
Maria Scott, 46, a housewife from Newcastle in northeast England, has been in place for 15 days.
"It's really important to show support because they need to know how much they are loved by the people," she told AFP.
"We're very proud of our monarchy."
The baby was born on St. George's Day, England's national day.
Tony Appleton, a town-crier dressed in a flamboyant red uniform, announced the news from the steps of the hospital to a crowd of supporters and media.
The birth was also announced on the display screen atop the 189-metre (620 feet) BT Tower in London, with the message "It's a boy!"
Meanwhile sailors and royal marines aboard HMS Albion lined up on the flight deck of the assault ship on operations in the Asia-Pacific region to spell out "boy!"
The baby boy is a sixth great-grandchild for Queen Elizabeth, who turned 92 on Saturday, and her husband Prince Philip.
He will hold the title of prince after the Queen changed the rules in 2012 to ensure that all of William's children would be entitled to the style, not just his eldest son.
As with their two other children, the royal couple did not know whether the baby was going to be a boy or a girl.
Bookmakers have Arthur, Albert, Frederick, James and Philip as their favourites for the young prince's name.
The boy does not overtake Charlotte in the line of succession due to new laws agreed across the 16 Commonwealth realms where Queen Elizabeth is the head of state, including Canada, Australia and New Zealand.
A night at the Lindo Wing costs £7,500 ($10,500, 8,550 euros), including a delivery package and two-room suite, excluding consultants' fees.
The birth was overseen by consultant obstetrician Guy Thorpe-Beeston, who is the surgeon gynaecologist to the royal household, and consultant gynaecologist Alan Farthing, the Queen's surgeon-gynaecologist.
They were part of the trusted team who also delivered George and Charlotte.
The duchess had suffered severe morning sickness during all three pregnancies.
William, who is destined to become king after Charles, and Kate met at St. Andrews University in Scotland.
They tied the knot at Westminster Abbey in London on April 29, 2011, in a ceremony watched by up to two billion people worldwide. The marriage helped breathe new life into Britain's monarchy after years of crisis.
The Sun newspaper reported Sunday that Kate's sister Pippa Middleton, 34, is pregnant with her first child.
The new royal baby's birth will be celebrated with a 41-gun salute in London's Hyde Park and The Tower of London will also fire 62 rounds.