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 pair said in a statement.
The couple 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 the Princess of Wales, the statement said.
Lilibet 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."
The message adds that anyone wishing to send gifts is asked to "support or learn more about" organisations working for women and girls.
Prime Minister Boris Johnson tweeted his "many congratulations" to the couple.
Prince Harry and Meghan married in May 2018 in a ceremony at Windsor Castle and welcomed their first child, Archie Harrison Mountbatten-Windsor, a year later. They quit their roles as senior working royals in March 2020 and now live in California.