Meghan Markle and Prince Harry 'Privately' Congratulate His Cousin Princess Eugenie on Pregnancy

Meghan and Harry publicly announced their own baby news three days after Princess Eugenie and Jack Brookbank's 2018 wedding

Meghan Markle and Prince Harry are sharing in his cousin Princess Eugenie's baby joy from across the pond.

A source tells PEOPLE that Harry and Meghan — who relocated to California earlier this year after stepping down from their senior roles within the royal family — have "sent their congratulations privately" to Princess Eugenie and her husband Jack Brooksbank after their announcement on Friday that they are expecting their first child.

The Duke and Duchess of Sussex publicly announced their own baby news — that they were expecting son Archie, born in May 2019 — three days after Princess Eugenie and Jack's wedding in October 2018.

Princess Eugenie and Prince Harry have always shared a unique bond, according to the new book Finding Freedom: Harry and Meghan and the Making of a Modern Royal Family.

"Eugenie had always been more than just a cousin to Harry. They were also the closest of friends," wrote authors Omid Scobie and Carolyn Durand. "Out of all the Queen's grandchildren, Harry and Eugenie have one of the most natural connections. Like Harry, Eugenie is loyal, honest, and great fun. The two had many nights out together in London."

Princess Eugenie; Meghan Markle and Prince Harry. Yui Mok - WPA Pool/Getty; Andrew Parsons - Pool/Getty

"Harry had always confided in his cousin when it came to the women in his life," they added. "Not only did he trust her implicitly, but friends say that she gives great advice and has always been 'beyond wise' for her years."

Prince Harry and Princess Eugenie. Max Mumby/Indigo/Getty

Prince Harry and Princess Eugenie. Pascal Le Segretain/Getty

This will be the first grandchild for Eugenie's parents, Prince Andrew and Sarah Ferguson, and Queen Elizabeth and Prince Philip's ninth great-grandchild.

In a statement, the palace said, "Her Royal Highness Princess Eugenie and Mr Jack Brooksbank are very pleased to announce that they are expecting a baby in early 2021."

"The Duke of York and Sarah, Duchess of York, Mr and Mrs George Brooksbank, The Queen and The Duke of Edinburgh are delighted with the news."

Jack Brooksbank and Princess Eugenie. Sarah Ferguson/Instagram

Princess Eugenie, 30, and Jack, 34, also shared their exciting baby news with a sweet Instagram post holding a fluffy pair of teddy bear slippers with the royal writing, "Jack and I are so excited for early 2021....👶🏻."

Fergie, as the royal mom-to-be's mother is known, expressed her delight about the family's new addition, saying in a statement to PEOPLE: "I am so excited by the news that Eugenie and Jack are expecting their first child. Thrilled for them both and in my 60th year cannot wait to be a grandmother. Welcoming a new baby into the York family is going to be a moment of profound joy."

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The baby news comes just two months after Eugenie's older sister, Princess Beatrice, wed Edoardo Mapelli Mozzi.

Updated by Simon Perry