The news was announced Friday morning in a press release from Kensington Palace which read: "The Duke and Duchess of Cambridge are delighted to announce that they have named their son Louis Arthur Charles".
Green co-leader Marama Davidson sung a waiata for the couple, which she said she wrote for her own children.
On Monday evening, 36-year-old Catherine - who also has four-year-old Prince George and two-year-old Princess Charlotte with Prince William - left St Mary's hospital in Paddington, London, and was pictured outside the ward with her 35-year-old spouse and their new arrival.
While the eldest of Kate and Wills brood had to return to school on Tuesday morning, Princess Charlotte only had to go to nursery on Thursday morning, which gave her more time to bond with her little brother.
The Duke and Duchess of Cambridge's third child was born on April 23, and now the newborn's proud father has signed the birth register at Kensington Palace, witnessed by Westminster City Council registrar Patricia Gordon. As in the past, the Duchess had a quick labour and Prince Louis was born at 11.01 at 8lbs 7oz.
The royal family's newest addition is likely a tribute to Prince Philip's late uncle Louis Mountbatten.
In honor of the anniversary, Kensington Palace posted a sweet throwback pic to Instagram Sunday of the couple driving away from their wedding in a convertible with a "JU5T WED" license plate.
Her Majesty The Queen was the first to be notified of the birth.
Prince Louis is fifth in line to the throne and is the first royal prince to not bypass an older sister in the line of succession.
Of course, with an elder brother in Prince George, the chances of either of the younger Cambridge children inheriting the throne now occupied by their great-grandmother are remote.
During the exchange, Kate can be heard saying William's full name - including his middle name Louis - and she can clearly be heard saying Loo-ee. It also bears Prince William's signature, which is exactly as aristocratic as you'd expect.
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