The Duchess of Cambridge’s sister gave birth on Monday afternoon to a boy weighing 8lb 9oz, with mother and baby said to be “doing well”.
Pippa and her husband, James Matthews, had been seen earlier in the day arriving at the private maternity wing of St Mary’s hospital in London. It is the same unit in which Kate gave birth to her three children.
She and William were the first to offer their congratulations.
Kensington Palace said in a short statement: “The Duke and Duchess of Cambridge are thrilled for Pippa and James.”
Pippa, who is 35, had announced her pregnancy only four months ago and had been keeping her friends up to date about her progress in a fitness column produced for the supermarket Waitrose.
She recently wrote: “As the final month nears and the bump grows prouder each day, movement is certainly getting more awkward.
“As a result, one of the biggest changes is that my lower body has tightened up.”
She surprised some commentators by her appearance on Friday at the wedding of Eugenie and Jack Brooksbank at Windsor Castle.
But despite her large baby bump she looked at ease when she joined the other guests – among them the Duke and Duchess of Sussex, Robbie Williams and the Hollywood actress, Demi Moore.
She and Mr Matthews married in May 2017 at St Mark’s Church, at Englefield Estate, Berkshire, near Bucklebury Manor, the Middleton family home.
Her husband is a former professional racing driver and now a hedge fund manager. He is the son of another race driver, David Matthews, a self-made millionaire who rose from his first job as a mechanic at his family’s garage in Yorkshire.