The Queen's 11th great-grandchild was born on Friday at a hospital in Santa Barbara, California.
Lilibet was born at 11:40am local time, weighed 7 lbs 11oz and is now "settling in at home".
Both mother and baby were doing well and were back at home, their press secretary said.
Lilibet is the Royal Family's nickname for Queen Elizabeth II, the baby's great-grandmother, the couple said. "Her middle name, Diana, was chosen to honour her beloved late grandmother, the Princess of Wales", the official statement from the couple said.
"When we think of her, we think of all the young women and girls around the globe who must be given the ability and support to lead us forward", she said. It means Prince Andrew, who was born as second in line in 1960, moves down to ninth place.
As for Meghan and Harry's choice to use "Lilibet" instead of the Queen's full first name, the reference is actually quite a personal one.
British Prime Minister Boris Johnson also sent a message of goodwill through Twitter, saying: "Many congratulations to the Duke & Duchess of Sussex on the birth of their daughter".
"Thank you for your continued kindness and support during this very special time for our family", the statement added.
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"On June 4th, we were blessed with the arrival of our daughter, Lili", they wrote.
Diana, the former wife of Prince Charles and mother to Harry and his elder brother William, died in a Paris vehicle crash in 1997. Their son Archie Harrison Mountbatten-Windsor was born a year later.
The photo was taken remotely via an iPad by a close friend and photographer, Misan Harriman.
Her grandfather, King George V, would affectionately call her Lilibet, imitating her own attempts to say her name.
He and Meghan quit their roles as senior working royals in March 2020. The Royal Family said the issue would be addressed privately.
"Lilibet" is the Queen's childhood nickname, which has stuck ever since.
"We can confirm that Archie is going to be a big brother", a spokesperson for the couple said in February. Even as a child, Queen Elizabeth, was also known to sign off her letters using "Lilibet" in the signature.
Harry, 36, has spoken recently about how the trauma of the loss was compounded when he had to walk as a 12-year-old behind his mother Diana's coffin in her funeral cortege under the glare of the world's media. But now the nickname will live on as a sweet tribute to the 95-year-old monarch in her newest granddaughter, Lilibet "Lili" Diana Mountbatten-Windsor. "We remain incredibly grateful".