Queen Elizabeth II and the royal family have congratulated Prince Harry and Meghan Markle on the birth of their daughter Lilibet 'Lili' Diana Mountbatten-Windsor, the monarch's 11th great-grandchild.

This is the second child for the couple, who have a two-year-old son named Archie Harrison Mountbatten-Windsor.

The royals, including Harry’s father Prince Charles and brother Prince William, were delighted with the news of the birth of the Duke and Duchess of Sussex's baby girl in Los Angeles on Friday, the Buckingham Palace said in a statement.

Harry and Meghan's second child is named after the Queen, who was affectionately nicknamed Lilibet by her family, and her late grandmother, Princess Diana, it said.

''Congratulations to the Duke and Duchess of Sussex on the birth of Lilibet Diana,'' the statement said.

''The Queen, the Prince of Wales (Charles) and The Duchess of Cornwall (Camilla) and the Duke and Duchess of Cambridge (William and Kate Middleton) are delighted with the news,'' it said.

William and Kate tweeted separately from their Kensington Palace Twitter account to say: ''We are all delighted by the happy news of the arrival of baby Lili. Congratulations to Harry, Meghan and Archie.'' 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.'' Lili is the first of the Queen's great-grandchildren to be born outside the United Kingdom as Harry and Meghan relocated to California in the US last year after they stepped back as frontline royals.

A statement from the couple's press secretary said that their second child was born at 11:40 am on Friday.

''It is with great joy that Prince Harry and Meghan, the Duke and Duchess of Sussex, welcome their daughter, Lilibet ‘Lili’ Diana Mountbatten-Windsor, to the world. Lili was born on Friday, June 4 at 11:40 am in the trusted care of the doctors and staff at Santa Barbara Cottage Hospital in Santa Barbara, California,” the statement said.

The new-born weighed 7 lbs 11 oz (3.48 kg), and both mother and child are said to be “healthy and well” and settling in at home, it said.

''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,” the official statement from the couple said. Harry and Meghan, who live in Montecito, are now on parental leave and on their official Archewell website, they have elaborated on the arrival of their baby daughter, it 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 statement said.

Lilibet was first used when Princess Elizabeth was a toddler and unable to pronounce her own name properly.

Her grandfather, King George V, would affectionately call her ‘Lilibet’, imitating her own attempts to say Elizabeth and from then on she became Lilibet, including to Prince Philip, the Queen’s late husband.