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The Princess of Cambridge was born on 2 May
The coins have a royal seal of approval from the Queen - who approved the decision during a meeting of the Privy Council at Buckingham Palace on 19 March - the Duke and Duchess of Cambridge, and the Chancellor.
John Bergdahl has designed the limited-edition pieces, and he was also the artist behind the commemorative coins which were minted for Prince George's birth in 2013.
The royal couple are expected to announce the Princess' name on Monday
The Royal Mint's Shane Bissett said: "It is only fitting that we commemorate this new addition to the Royal Family with the release of a special coin, just as we celebrated the arrival of Prince George."
When George arrived in July 2013, The Royal Mint produced 10,000 solid silver crown-sized £5 coins – which cost £80 each – and 2,013 22 carat gold sovereigns, priced at £800 each.
Both coins, which featured the newborn's namesake St George, were sold out within days.
In addition to the £5 coin, the Royal Mint has also produced 2015 silver pennies which will be given to babies born on the same day as the Princess.
Babies born on the same day as Prince George were also given their own royal gift in the form of a lucky silver coin. The Royal Mint struck a total of 2,013 silver coins and presented them, free of charge, to the tots who shared George's birthday. Depending on the sex of the child, the coin was delivered in a pink or blue pouch.
The royal couple are yet to reveal the name of their baby daughter, but it is expected to happen after the Queen is introduced to the Princess on Monday at Anmer Hall, William and Kate's official country residence.