Prince Harry and Meghan announced that the infant, a first sibling for Archie, was born on Friday in California.
Lili is named after her great-grandmother the Queen – who was affectionately nicknamed Lilibet by her family – and her grandmother, the late Princess Diana.
A Buckingham Palace spokesperson said: “The Queen, The Prince of Wales and The Duchess of Cornwall, and The Duke and Duchess of Cambridge have been informed and are delighted with the news of the birth of a daughter for The Duke and Duchess of Sussex.”
A statement from the couple’s press secretary said that she was born at 11.40 am on Friday “in the trusted care of the doctors and staff at Santa Barbara Cottage Hospital in Santa Barbara, California”.
She weighed 7lbs 11oz (3.5kg) and she and Meghan are said to be “healthy and well, and settling in at home”.
Harry and Meghan, who live in Montecito, said on their Archewell website: “On June 4, we were blessed with the arrival of our daughter, Lili.
