As the Duke and Duchess of Cambridge leave St Mary’s Hospital in London with their newborn son, Kate Middleton says the birth was “very emotional”.
With cheering crowds greeting them, Prince William said the baby, wrapped in a white blanket, was a “big boy” with a “good pair of lungs on him”.
He said they were “working on” a name for him and that he had inherited his wife’s looks “thankfully”.
The Duchess of Cambridge, Kate Middleton, said the birth had been “very emotional …. any parent would know what this feels like.”
Just before they appeared in public, the Queen said she was “thrilled” by the birth, according to a guest at a Buckingham Palace reception on Tuesday night.
Earlier, Prince Charles and his wife, the Duchess of Cornwall, travelled from east Yorkshire to see the couple and their son.
They were preceded by Carole and Michael Middleton, Kate’s parents, who were the first to visit the hospital following the birth on Monday.
After spending just over an hour there, Mrs Middleton told the media the baby was “abolutely beautiful”, adding: “They are both doing extremely well and we are so thrilled.”
Asked if she had suggested a name, she replied: “Absolutely not, but thank you.”
It was the first visit the royal couple and their son had received since the newborn was delivered on Monday at 4.24pm, weighing 8lb 6oz.
William, Kate and their son are expected to leave hospital on Tuesday evening.
A spokesman for the palace said on Tuesday morning: “Mother, son and father are all doing well this morning.”
The Duke and Duchess of Cambridge have also thanked staff at the hospital. In a statement from Kensington Palace, they 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.”
A spokesman for Kensington Palace has said: “Mother, son and father are all doing well this morning.” #RoyalBabyBoy
— Clarence House (@ClarenceHouse) July 23, 2013
The Prince of Wales and the Duchess of Cornwall have said they were “so thrilled” for the parents on the birth of their baby boy.
They added: “Grandparenthood is a unique moment in anyone’s life, as countless kind people have told me in recent months, so I am enormously proud and happy to be a grandfather for the first time and we are eagerly looking forward to seeing the baby in the near future.”
The duchess praised Charles when they visited the village of Bugthorpe in East Yorkshire.
She said: “It’s very exciting and it’s wonderful for the grandfather – he’s brilliant with children.”
There was a musical tribute to the newborn prince at the palace on Tuesday, as members of the Scots Guards band performed Congratulations following the changing the guard ceremony (see video above).
Some of those in the crowd who packed outside the palace gates and at the Victoria Memorial sang along, while the ensemble broke into spontaneous applause at its conclusion.
Trafalgar Square’s famous fountains were lit with blue lights on Monday night and London Mayor Boris Johnson said this will continue for the next six days in celebration of the royal birth.
“Huge congratulations to the duke and duchess on the birth of their first child who will, by virtue of being born in this great city, be a Londoner through and through,” he said.
“I am sure millions of Londoners will be raising a glass today to toast this wonderful news.”
David Cameron offered his congratulations on Twitter. He wrote: “I’m delighted for the duke and duchess now their son has been born.
“The whole country will celebrate. They’ll make wonderful parents.”
US President Barack Obama and his wife Michelle have congratulated the Duke and Duchess of Cambridge on the “joyous occasion of the birth of their first child”, adding: “We wish them all the happiness and blessings parenthood brings”.
Meanwhile, Oliver Hicks, 31, a close friend of Prince William, said he was thrilled to hear the “fantastic” news.
Read more: when will the new heir inherit the throne?
Celebrations will continue today as the nation waits for the palace to announce the name. The palace have said they will make the announcement “in due course”.
The Duke and Duchess of Cambridge, however, are expected to pick a traditional royal name for their newborn baby prince.
Royal infants mostly have historical names which are passed down through the generations.
The baby, who will eventually be King, will be styled HRH Prince (forename) of Cambridge. Should he require a surname, such as on marriage, it will be Mountbatten-Windsor.
One day the baby is also likely to become the Prince of Wales. The title is usually given to the male heir to the throne, but is not automatic.
Royal babies also usually have a number of middle names. The Prince of Wales has four names, as does William.
Read more: how royal is the royal baby?
The King’s Troop Royal Horse Artillery and the Honourable Artillery Company carried out the ceremonial royal salutes in honour of the new addition to the royal family (see video below).
Gun salutes are fired for the birth of every prince or princess, no matter where their place is in the line of succession.
The King’s Troop Royal Horse Artillery, wearing full dress uniform, rode past Buckingham Palace to Green Park where they staged a 41-gun royal salute.