The King’s niece said she was born in hospital in Lisbon and weighed 6lbs 9oz.
Posting on Instagram, Eugenie said she and husband Jack Brooksbank were “beyond in love with our girlie”.
The couple already have two boys, five-year-old August, and three-year-old Ernest.
It’s understood they are taking their time to choose a name for their daughter – who is now 15th in line to the throne.
Buckingham Palace said the couple were “delighted to announce the safe arrival of their daughter” and that she was born on 3 August at 6.20pm.
“Their Majesties The King and Queen and other members of the royal family were delighted to be informed of the news,” the statement added.
The princess and her husband have a home and other connections in Portugal.
The new arrival is Andrew Mountbatten-Windsor’s fifth grandchild; Princess Beatrice has two girls and a stepson with her husband Edoardo Mapelli Mozzi.
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