Kate Middleton has given birth to a girl at St Mary’s Hospital in London on May 2nd.
The name of the baby will be announced in due course, the Kensington Palace said.
Prince George’s name was announced two days after his birth, which is a relatively quick turnaround compared with previous royal babies.
Prince William’s name was announced after 7 days in 1982, and there was a wait of a month following Prince Charles’s birth in 1948.
The new royal will not be overtaken in the line of succession by any future younger brothers.
Under new rules which came into force in March, male bias was removed from the succession rules.
She will also be known as the Princess of Cambridge after a Letter Patent was issued by Queen Elizabeth II.
It declared: “All the children of the eldest son of the Prince of Wales should have and enjoy the style, title and attribute of royal highness with the titular dignity of prince or princess prefixed to their Christian names or with such other titles of honor”.
The princess will also be able to marry a Roman Catholic without losing her place in line to the throne.