Congratulations Prince Harry & Meghan Markle!
Lilibet "Lili" Diana Mountbatten-Windsor was born on Friday morning in a hospital in Santa Barbara, California.
Both mother and child are healthy and well, the couple said in a statement.
Buckingham Palace 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."
Prince Harry and Meghan said they named their second child Lilibet after the Royal Family's nickname for the Queen, the baby's great-grandmother.
Her middle name, Diana, was chosen to honour her "beloved late grandmother", the Princess of Wales, the statement said.
Lilibet was born at 11:40am local time, weighed 7 lbs 11oz and is now "settling in at home".
She is the Queen's 11th great-grandchild and is eighth in line to the throne. It means Prince Andrew, who was born as second in line in 1960, moves down to ninth place.
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."
The message adds that anyone wishing to send gifts is asked to "support or learn more about" organisations working for women and girls.
They have not released any photos of their daughter.