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Meghan gave birth to her 7lb 11oz daughter, on Friday in California at Santa Barbara Cottage Hospital and both mother and child are healthy and well, Meghan's press secretary said.
She is the couple's second child, after Archie Harrison Mountbatten-Windsor, who is aged two.
A statement from the couple's press secretary said: "It is with great joy that Prince Harry and Meghan, The Duke and Duchess of Sussex, welcome their daughter, Lilibet ‘Lili’ Diana Mountbatten-Windsor, to the world.
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"Lili was born on Friday, June 4 at 11.40am in the trusted care of the doctors and staff at Santa Barbara Cottage Hospital in Santa Barbara, California.
"She weighed 7lbs 11oz. Both mother and child are healthy and well, and settling in at home.
"Lili is named after her great-grandmother, Her Majesty The Queen, whose family nickname is Lilibet.
"Her middle name, Diana, was chosen to honour her beloved late grandmother, The Princess of Wales.
"This is the second child for the couple, who also have a two-year-old son named Archie Harrison Mountbatten-Windsor.
"The Duke and Duchess thank you for your warm wishes and prayers as they enjoy this special time as a family."
In a message of thanks from Meghan and Harry on the 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."
Harry and Meghan spoke about expecting a girl in March during their tell-all interview with Oprah Winfrey.
The baby is the most senior royal in the current line of succession to be born overseas and would be eligible to become president of the United States.
Her arrival follows the heartache the couple suffered when the 39-year-old duchess suffered a miscarriage in the summer of 2020.
In November, former Suits actress 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.
Home for the new family-of-four is Harry and Meghan's £11 million forever mansion in Montecito, California.