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The certificate filed on Friday makes clear that Meghan did not give birth to the child in the couple's Frogmore Cottage home, on the Windsor Castle estate, as had been rumoured.
Archie Harrison Mountbatten-Windsor was born at the Portland Hospital in central London on May 6.
He is seventh in line for the British throne.
Harry and Meghan announced weeks before the birth that they wanted to keep many details of his birth private.
Meghan's name is listed on the birth certificate as Rachel Meghan Her Royal Highness The Duchess of Sussex.
She is a former actress from the United States.