The Duke and Duchess of
Cambridge have thanked hospital staff for their "tremendous" care, as
the world awaits the first glimpse of their baby son.
A Kensington Palace spokesman said: "Mother, son and father are all doing well."It is understood the family will leave hospital on Tuesday evening or on Wednesday morning.
The birth of the third in line to the throne will be marked later with a series of gun salutes.
Prince William was at the private Lindo Wing of St Mary's Hospital, in west London, for the birth at 16:24 BST on Monday, and stayed with his wife and son overnight.
In a statement, the couple said: "We would like to thank the staff at the Lindo Wing and the whole hospital for the tremendous care the three of us have received.
"We know it has been a very busy period for the hospital and we would like to thank everyone - staff, patients and visitors - for their understanding during this time."
Prince William had earlier said the couple "could not be happier" following the birth of the 8lb 6oz boy.
At Buckingham Palace, royal watchers and
tourists are queuing in the rain to catch a glimpse of the bulletin
announcing the arrival of the royal baby, which is being displayed on an
easel.
The news broke about four hours after the birth and the
notice is to be displayed for 24 hours, which means it is likely to be
removed just after 20:00.Guardsmen outside the palace have brought a celebratory feel to the proceedings ahead of the Changing of the Guard, playing "Congratulations" to the crowd.
Fresh from trying to get her photo of the easel, Robyn Holtham, 41, from Oxfordshire, described the birth as fantastic news.
"The Royal Family has been becoming more accessible with Kate and William, people can identity with them. Kate is a more normal person. They're just people who like to have fun and do normal things," she said.
'Knocked back' The world now awaits the couple's choice of names for their son, with George the bookmakers' favourite, followed by James and Alexander.
Nicholas Witchell said the scale of the international interest was "pretty awesome", and "quite threatening in a sense". He said the couple would be "knocked back" when they step out of the hospital.
The arrival generated headlines and celebrations around the world, and prompted messages of goodwill to flood in:
- New Yorkers were informed of the news when it was tickered in lights at Times Square
- In London, Trafalgar Square was lit blue for a boy, while the BT Tower delivered the message: "It's a boy!"
- At its peak, there were more than 25,000 tweets per minute about the royal baby's birth
- US president Barack Obama said: "We wish them all the happiness and blessings parenthood brings" while Australian PM Kevin Rudd said Australians wished "the royal bub all the best"
- The Archbishop of Canterbury, Most Reverend Justin Welby, greeted the news by saying: "Along with millions here and around the world, I share in their joy at this special time"
- A specially-filmed scene will be inserted into Tuesday's edition of EastEnders to mark the occasion
Following the birth announcement, a statement from Kensington Palace said the Royal Family were "delighted".
The Duchess of Cornwall, on a two-day visit to Yorkshire with
the Prince of Wales, said it was a "wonderfully uplifting moment for
the country" and that mother and baby were "doing well". The prince said he was "thrilled and very excited", as the couple were congratulated by well-wishers during a walkabout.
Meanwhile, Princess Anne said the arrival of the Royal Baby was "nothing to do with me, but it's very good news".
Royal doctor Mr Setchell described the new arrival as a "wonderful baby, beautiful baby".
The birth of the prince means the monarchy has three generations of heirs to the throne for the first time since 1894.
Nicholas Witchell said the third in line to the throne could expect to be brought up in a "secure and loving environment", shielded from many of the pressures of ordinary life but facing the specific challenges his position will bring.
The baby's future, he said, will be "a lifetime of public curiosity and, in due course, the responsibility of refreshing and taking forward the ancient institution that is the world's best-known hereditary monarchy".