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The couple took their daughter home after spending just over 12 hours at the hospital
The Queen has met her new great-granddaughter Princess Charlotte for the first time at Kensington Palace.
The princess, who is fourth in line to the throne, was born on Saturday at London’s St Mary’s Hospital, weighing 8lbs 3oz (3.7kg).
Kensington Palace revealed on Monday that she had been named Charlotte Elizabeth Diana.
The Duke and Duchess of Cambridge have formally registered the birth of their second child.
The Duke of Cambridge signed the birth register at Kensington Palace on Tuesday, witnessed by a registrar from Westminster Register Office.
The document gives the date and place of Princess Charlotte’s birth, and her full name as Her Royal Highness Princess Charlotte Elizabeth Diana of Cambridge.
The Queen and other senior royals were told of the baby’s name before the announcement was made public.
The King’s Troop Royal Horse Artillery marked the arrival of the princess with a 41-round gun salute
Charlotte, the feminine form of Charles, has a long royal pedigree and became popular in the 18th Century when it was the name of George III’s queen.
The King bought Buckingham House in 1761 for his wife Queen Charlotte to use as a family home close to St James’s Palace – it became known as the Queen’s House and is now Buckingham Palace.
According to figures from the Office for National Statistics, Charlotte is the 21st most popular girl’s name in England and Wales with 2,242 babies being given it in 2013.
The Queen is believed to have arrived in London from her Sandringham estate in Norfolk.
The princess has had several other visitors, including the Prince of Wales and Duchess of Cornwall who spent more than an hour with their new granddaughter on Sunday.
The Duchess of Cambridge’s parents, Michael and Carole Middleton, and sister Pippa have also met their newest relative.
On Monday, gun salutes took place in London to mark the birth. Gun salutes are a tradition on the birth of every prince or princess.
Soldiers from The King’s Troop Royal Horse Artillery rode out in a procession from Wellington Barracks, near Buckingham Palace, to sound 41 shots in Hyde Park .
At the same time, the Honourable Artillery Company left their Armoury House barracks in the City of London to fire a 62-gun salute at the Tower of London.
© BBC