Lilibet "Lili" Diana Mountbatten-Windsor was born at 11.40am at Santa Barbara Cottage Hospital in California on Friday, June 4.
The baby – a younger sister for the Sussexes’ two-year-old son Archie Mountbatten-Windsor – weighed 7lb 11oz.
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."
Lili is the first of the Queen's great-grandchildren to be born outside the UK.
She is the Queen's 11th great-grandchild and is eighth in line to the throne.
In a message of thanks on the couple's Archewell website, they said: "On June 4, we were blessed with the arrival of our daughter, Lili.
"She is more than we could have ever imagined, and we remain grateful for the love and prayers we've felt from across the globe.
"Thank you for your continued kindness and support during this very special time for our family."
Lili's birth comes three months after her parents gave an explosive interview to Oprah Winfrey about their treatment from the media and the Royal Family.
Among the allegations were that a member of the family - not the Queen or the late Duke of Edinburgh - had raised concerns about the colour of Archie's skin before he was born in May 2019.
The Queen responded by saying the issues were taken “very seriously” but that “some recollections may vary” and the matter would addressed by the family privately.
Meghan also revealed late last year that she had a miscarriage in July 2020
In November, Meghan wrote, in a deeply personal article for the New York Times: "I knew, as I clutched my firstborn child, that I was losing my second.!
The Sussexes announced on Valentine's Day they were expecting again, releasing a black and white photo of themselves sitting under a tree in Los Angeles.
Harry and Meghan stepped down as senior working royals in March 2020 in a quest for personal and financial freedom after struggling with royal life.
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