According to reports, the latest addition to the family was born yesterday at 1.58pm, weighing a healthy 8lb 9oz.
It was Pippa's second Royal Wedding of the year, after she attended The Duke and Duchess of Sussex's nuptials in May.
The new baby will have plenty of playmates around; in addition to Middleton and William's kids - Prince George, Princess Charlotte and Prince Louis - Matthews' younger brother, Spencer Matthews, welcomed his own first child with his wife Vogue Williams in September.
The luxury ward provides a premium service for expectant and new mothers, with all patients provided a private room with an ensuite, which comes with phones and fridges.
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How much did Pippa's baby weigh at birth?
She and her husband financier husband James Matthews are said to be "delighted".
What will the baby be called?
Pippa, who became a household name after serving as Kate's bridesmaid during the Royal Wedding in 2011, married hedge fund manager James previous year.
First to publicly congratulate them were Kate and William.