Princess Charlotte, who is just four days old, left her Kensington Palace home in London to spend the next few weeks at Anmer Hall in Norfolk county in the east of England.
The Duke and Duchess of Cambridge were seen leaving London in convoy in their Range Rover to spend time at the refurbished Georgian mansion on the Queen's private Sandringham estate.
William was at the wheel and Kate in the passenger seat, with Prince George and Princess Charlotte strapped into baby seats at the back.
The 10-bedroom Anmer Hall was a gift for William's family from his grandmother, Queen Elizabeth II, who saw her newest granddaughter for the first time on Tuesday.
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William is on two weeks paternity leave from his job as an air ambulance helicopter pilot and is expected to start the final phase of his training at the beginning of June.
The new baby, who is fourth in line to Britain's throne, has been named Charlotte Elizabeth Diana and will be known as Her Royal Highness Princess Charlotte of Cambridge.
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.
Elizabeth is an ode to the name of the current Queen of England and Diana a tribute to the memory of William's late mother.