The Queen is due back in London on Tuesday and it is thought she will meet her new great-granddaughter for the first time.
Princess Charlotte Elizabeth Diana was born on Saturday but the Queen has been in Yorkshire on royal duties.
The latest addition to the royal family is the monarch's fifth great-grandchild.
In the next few days William and Kate are expected to head to Sandringham where they will spend time as a family for the first few weeks of Charlotte's life.
Bookies have had to pay out an estimated £1 million following the announcement the Duke and Duchess of Cambridge have named their second child Charlotte Elizabeth Diana.
Ladbrokes said Charlotte was the most popular bet since the princess was born - with three times as many wagers placed as other favourites Alice, Diana and Olivia.
Jessica Bridge, of Ladbrokes, said: "Charlotte was the hot tip over the weekend and royal watchers up and down the land are quids in.
"We may have lost a fortune but we're paying out with a smile and wish the Duke and Duchess all the best."
Coral called it "one of the most costliest results in royal betting history."
A woman from Barnes, south west London, is due to pick up £1,400 was the biggest winner at William Hill. She put £400 down at 5-2 that the baby would be called Charlotte.
Naming the royal baby Charlotte Elizabeth Diana will be seen as a tribute to the Duke of Cambridge's father, mother and grandfather.Read the full story ›
The Duke and Duchess of Cambridge have named their daughter Charlotte Elizabeth Diana.
She will be known as HRH Princess Charlotte of Cambridge, Kensington Palace have announced.
The name Charlotte had been a favourite with the bookies during the week but in the last few days had been pushed into second place by Alice.
But betting firms have said they would face a huge payout if any of the heavily backed top five names were chosen by the Cambridges.
Video shows a 62-gun salute at the Tower of London marking the birth of the Duke and Duchess of Cambridge's second child and new daughter.
Royal gun salutes have been fired to celebrate the birth of the Duke and Duchess of Cambridge's baby princess.
The Honourable Artillery Company completed a 62-gun salute at the Tower of London - an extra 21 for the City of London - while the King's Troop Royal Horse Artillery silmultaneously fired 41 volleys in Hyde Park at 2pm.
Just before the King's Troop began the Royal Artillery Band played the Stevie Wonder hit 'Isn't She Lovely'.
The bells of Westminster Abbey also rang out at exactly 2pm to mark the royal birth.
Royal gun salutes will be fired today to mark the birth of the Duke and Duchess of Cambridge's baby princess.
The King's Troop Royal Horse Artillery will fire 41 volleys in Hyde Park to coincide with the Honourable Artillery Company's 62-gun salute at the Tower of London - an extra 21 for the City of London.
The soldiers, horses and guns of the King's Troop will ride out in procession from their forward mounting base in Wellington Barracks through London and to the north of Hyde Park to fire the volleys.
They will be accompanied by music from the Royal Artillery Band and their 71 horses will pull six First World War-era Ordnance Quick Fire 13-pounder field guns.
The HAC will leave their barracks at Armoury House pulling three Ceremonial 105mm Light Guns with their liveried Pinzgauer vehicles and drive through the City with an escort to the Tower of London.
The weapons will be fired from Gun Wharf, overlooking HMS Belfast.
Prince Harry has spoken of his excitement at the arrival of his new niece in a statement issued by Kensington Palace.
Harry, who is currently on secondment with the army in Australia, said: "She is absolutely beautiful. I can't wait to meet her."
Prince Harry has said about his new niece: "She is absolutely beautiful. I can't wait to meet her." http://t.co/HiNR8lzThy
The Duke and Duchess of Cambridge are "hugely grateful" for the messages of congratulations they have received following the birth of their daughter, a palace spokesperson said today.
Kensington Palace posted a message on behalf of the couple on its official Twitter page:
The Duke and Duchess are hugely grateful for the messages of congratulations they have received from people all over the world 1/2
It means a great deal to them that so many people have celebrated the arrival of their new daughter 2/2 http://t.co/RDxkAip0VC
Prince Charles waved the waiting crowd as he drove away from Kensington Palace with his wife Camilla.
The couple were thought to have been introduced to their new granddaughter.