The couple said Lilibet Diana was born Friday at California's Santa Barbara Cottage Hospital, weighing in at 7 pounds, 11 ounces.
"Both mother and child are healthy and well, and settling in at home," a statement on the couple's website said.
"Lili is named after her great-grandmother, Her Majesty The Queen, whose family nickname is Lilibet. Her middle name, Diana, was chosen to honor her beloved late grandmother, The Princess of Wales."
Late Sunday, the official Twitter account of the royal family said: "Congratulations to The Duke and Duchess of Sussex on the birth of Lilibet Diana!
"The Queen, The Prince of Wales and The Duchess of Cornwall and The Duke and Duchess of Cambridge are delighted with the news. Lilibet is Her Majesty's 11th great-grandchild."
Diana was Harry's mother, who died in a Paris car crash in 1997.
Harry, 36, and Meghan, 39, married in 2018 and are the parents of a 2-year-old son named Archie.
They first disclosed they were expecting a second child in February.
The couple announced in 2020 that they were stepping down as senior members of the British royal family and moving to North America.
Since stepping away from their royal duties, Harry has been working with media mogul Oprah Winfrey to spotlight mental-health issues, while Markle has a children's book coming out soon. They are also developing programs for Netflix.