A heartfelt message posted to their Twitter account on Sunday evening read: "We are all delighted by the happy news of the arrival of baby Lili. Congratulations to Harry, Meghan and Archie."
Earlier in the day, a joint statement from Buckingham Palace on behalf of senior royals read: "The Queen, The Prince of Wales and The Duchess of Cornwall, and The Duke and Duchess of Cambridge have been informed and are delighted with the news of the birth of a daughter for The Duke and Duchess of Sussex."
WATCH: Harry and Meghan welcome baby daughter and name her Lilibet 'Lili' Diana
Harry and Meghan's daughter, who was born on 4 June, is the second niece for the Cambridges after Kate's sister, Pippa Middleton, welcomed baby number two in March.
Pippa and her husband, James Matthews, who are already parents to two-year-old Arthur, named their daughter, Grace Elizabeth Jane.
William and Kate are also uncle and aunt to the Sussexes' first born child, Archie Harrison Mountbatten-Windsor, who turned two in May.
Kate and Louis with Meghan and Archie in summer 2019
Relations between the Duke of Cambridge and the Duke of Sussex have been strained for the past couple of years, with Harry first addressing rumours of a rift in Tom Bradby's 2019 documentary Harry and Meghan: An African Journey.
When asked by the reporter at the time whether there was any truth to the reports, Harry said, "Inevitably stuff happens" but that there was little truth to the speculation, saying: "The majority of the stuff is created out of nothing but as brothers, you know, you have good days, you have bad days."
The Cambridges congratulated the Sussexes on the birth of their baby girl
And in Harry and Meghan's tell-all interview with Oprah Winfrey in March, the Duke of Sussex said of his brother: "I love William to bits, he's my brother, we've been through hell together but we're on different paths." He later added: "The relationship is space at the moment, and time heals all things."
William and Harry were recently reunited at the Duke of Edinburgh's funeral in April, where cameras spotted the pair walking and talking together with Kate after the moving service.
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