The royal, who welcomed her first child earlier this year, took to her Instagram Stories to share the sweet message, alongside the picture the couple shared to announce Meghan's pregnancy.
WATCH: Harry and Meghan welcome baby daughter and name her Lilibet 'Lili' Diana
"Congratulations dear cousins… we couldn't be happier for you all," she wrote alongside six red love heart emojis.
Prince Andrew and Sarah Ferguson's message came hours after Buckingham Palace released a statement on behalf of the Queen and the senior royals that 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."
They later all took to Twitter and Instagram to share their individual messages, each alongside a different photo.
Princess Eugenie posted a beautiful message to her cousins
Prince William and Kate shared a picture of the family of three, taken by Misan Harriman for Vogue, and wrote: "We are all delighted by the happy news of the arrival of baby Lili. Congratulations to Harry, Meghan and Archie."
Grandfather Prince Charles and the Duchess of Cornwall shared a picture of the family of three taken during their last tour as royals and added: "Congratulations to Harry, Meghan and Archie on the arrival of baby Lilibet Diana. Wishing them all well at this time."
Lilibet 'Lily' Diana Mountbatten-Windsor is Prince Charles's fifth grandchild and the Queen's 11th great-grandchild.