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, Prince Harry and Meghan 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 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.
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 stated 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.
Prime Minister Boris Johnson tweeted his "many congratulations" to the couple and Labour leader Sir Keir Starmer welcomed the "wonderful news".
Prince Harry and Meghan met on a blind date and married in May 2018 in a ceremony at Windsor Castle. They welcomed their first child, Archie Harrison Mountbatten-Windsor, a year later.
Meghan's friend, Misan Harriman, who took black-and-white photographs of the couple for their pregnancy announcement, tweeted his congratulations: "Lilibet has arrived! Congratulations to my brave friend and her lovely family!"
The couple quit their roles as senior working royals in March 2020 and now live in California.
Their statement said it was with "great joy" that they welcomed Lilibet "Lili" Diana Mountbatten-Windsor to the world.
"The Duke and Duchess thank you for your warm wishes and prayers as they enjoy this special time as a family."