The little girl weighed 6lbs 7oz.
Grace’s middle names are a nod to her grandmothers – Carole Elizabeth Middleton and Jane Matthews. Elizabeth could perhaps be a nod to the family’s royal ties.
A source told Hello! “Mother and baby are doing well. She’s perfect, everyone is overjoyed at such a happy arrival.”
Pippa and hedge fund billionaire James, 45, married in 2017. They live in a £17 million home in London and are parents to two-year-old son, Arthur.
Pippa was last seen in public on Friday.
Grandmother Carole Middleton confirmed Pippa was pregnant for a second time in an interview with Good Housekeeping magazine a few weeks ago.
“I hope to see more of my family than I could last year, including, of course, my new grandchild,” she revealed.
But rumours of Pippa’s second pregnancy first swirled shortly before Christmas when Page Six reported the couple were expecting another baby.
A source said: “Pippa and James are thrilled, it’s fantastic news amid a difficult year. The entire family is delighted.”
Pippa has never commented on her pregnancy and prefers to keep a low public profile.
It comes after the Cambridge family shared a Mother’s Day post revealing cards made by Prince George, seven, Princess Charlotte, five, and Prince Louis, who is almost two, for their late “Granny Diana.”
At the weekend, Kate also visited a vigil in south London for Sarah Everard who was killed while walking home in Clapham earlier this month.