The Duke and Duchess of Sussex are settling into life as a family of four after the birth of their daughter Lilibet “Lili” Diana.

Meghan and Harry said it was a “very special time” and described the baby girl as “more than we could have ever imagined”.

Lili, a younger sister for the Sussexes’ two-year-old son Archie Mountbatten-Windsor, was born at 11.40am on Friday June 4 at Santa Barbara Cottage Hospital in California weighing in at 7lb 11oz.

The Queen, the Prince of Wales and the Duchess of Cornwall, and the Duke and Duchess of Cambridge’s social media accounts shared their congratulations on the happy news.

Lilibet is the Queen’s family nickname and the choice pays tribute to the monarch at a challenging time for the Windsors, who are mourning the loss of the Duke of Edinburgh.

They have also faced heartbreak and division after the Sussexes, who quit as senior working royals last year, plunged the monarchy into crisis with their bombshell Oprah Winfrey interview.

Harry made further controversial comments about his family in the following weeks, and has also experienced a long-running rift with his brother William.

William and Kate’s official Twitter account posted a message saying: “We are all delighted by the happy news of the arrival of baby Lili. Congratulations to Harry, Meghan and Archie.”

The Prince of Wales and the Duchess of Cornwall’s account also welcomed “baby Lilibet Diana”, adding: “Wishing them all well at this special time.”

The monarchy’s official Twitter account shared an image from Harry and Meghan’s wedding day, celebrated the arrival, and noted that the baby was the Queen’s 11th great-grandchild.

It also echoed an earlier statement from a Buckingham Palace spokeswoman, saying: “The Queen, The Prince of Wales and The Duchess of Cornwall and The Duke and Duchess of Cambridge are delighted with the news.”

In a message of thanks on their Archewell website, Harry and Meghan 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 Sussexes’ press secretary confirmed the baby had been named Lilibet “Lili” Diana Mountbatten-Windsor.

She added: “Both mother and child are healthy and well, and settling in at home.

“Lili is named after her great-grandmother, Her Majesty the Queen, whose family nickname is Lilibet.

“Her middle name, Diana, was chosen to honour her beloved late grandmother, the Princess of Wales.”

Harry had long been expected to honour his late mother Diana, Princess of Wales, who died in a car crash when he was 12.

The couple’s spokeswoman added: “The duke and duchess thank you for your warm wishes and prayers as they enjoy this special time as a family.”

Harry and Meghan are now on parental leave, their website said.

The new baby is the Queen’s 11th great-grandchild, and the first to be born since Philip’s death.

But with the Sussexes living in California and amid troubled relationships with Harry’s family, it is not known when or if the new addition will meet the Queen and the rest of the royals.

The duke has accused his family of “total neglect” when Meghan was feeling suicidal amid harassment on social media.

In his Apple TV mental health series, he lambasted the parenting skills of the Prince of Wales, criticising his father for expecting his sons to endure the pressures of royal life, just as Charles has done, instead of protecting them.

Just like Archie was not entitled to be a prince or an HRH when he was born in 2018, the Sussexes’ daughter is not permitted to be a princess or an HRH due to rules set down more than 100 years ago by George V.

Meghan controversially claimed during the Oprah broadcast that Archie had his right to be a prince taken away from him because of his race.

In fact, he was too far removed from the crown because although he is a great-grandchild of a sovereign, he is not the “eldest living son of the eldest son of the Prince of Wales”, as George V’s rules required.

Lili will be entitled to be a princess and Archie a prince, both with HRH styles, after the death of the Queen and when Charles becomes king.

This is because they will have moved up the line of succession to become the children of a son of a monarch.

Despite Harry and Meghan quitting as senior working royals, the baby still has a place in the line of succession.

She is eighth in line to the throne, coming after Archie, who is seventh, and before the Duke of York, who has dropped to ninth.

The new baby is also a first cousin of Prince George, Princess Charlotte and Prince Louis and a fifth grandchild for Charles, but will grow up across the Atlantic, thousands of miles away from the royal family.

Lili is the most senior royal in the line of succession to be born overseas and would be eligible to become president of the United States.

Her arrival follows the heartache the couple suffered when the 39-year-old duchess suffered a miscarriage in summer 2020.

In November, former Suits actress Meghan wrote in the New York Times: “I knew, as I clutched my firstborn child, that I was losing my second.”

The Sussexes announced on Valentine’s Day that they were expecting again, releasing a black and white photo of themselves sitting under a tree in Los Angeles.

Harry and Meghan stepped down as senior working royals in March 2020 in a quest for personal and financial freedom after struggling with royal life.

They have signed multi-million-pound deals with Netflix and Spotify, and set up their Archewell Foundation.

If Harry keeps true to his pledge, their daughter will be their last child.

He told activist and chimpanzee expert Jane Goodall in 2019 that he would only have two children for the sake of the planet.

Home for the new family-of-four is Harry and Meghan’s £11 million mansion in Montecito, California.