Princess Beatrice's sister Eugenie - who married Jack Brooksbank at Windsor Castle last year - posted her congratulations on Instragram saying they were "meant to be".
Sarah Ferguson took to social media to congratulate the couple, and the Duke and Duchess of York have spoken of their pride at the news in a statement released by Buckingham Palace.
They said: "We are thrilled that Beatrice and Edoardo have got engaged, having watched their relationship develop with pride.
"We are the lucky parents of a wonderful daughter who has found her love and companion in a completely devoted friend and loyal young man.
"We send them every good wish for a wonderful family future."
Mr Mozzi's family have also praised his and Beatrice's "wonderful relationship".
Nikki Williams-Ellis and Alessandro Mapelli Mozzi said: "We are truly delighted about Edoardo and Beatrice's engagement. Our family has known Beatrice for most of her life.
"Edo and Beatrice are made for each other, and their happiness and love for each other is there for all to see.
"They share an incredibly strong and united bond, their marriage will only strengthen what is already a wonderful relationship."
Edoardo, 34, will be welcomed to the Royal Family next year, but has Italian blue blood himself.
His father is Count Alessandro Mapelli Mozzi, who represented Britain as a skier – but he was educated at Radley in Oxfordshire before studying for a Master's in politics at Edinburgh.
He and the princess, 31, were first pictured together after Princess Eugenie's wedding.
Then in March they were pictured holding hands in New York before making an official appearance at the National Portrait Gallery Gala.
It is understood they met in September last year. Mr Mozzi has a child from a previous relationship - a toddler son called Wolfie.
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Edoardo, 34, will be welcomed to the Royal Family next year, but has Italian blue blood himself.
His father is Count Alessandro Mapelli Mozzi, who represented Britain as a skier – but he was educated at Radley in Oxfordshire before studying for a Master's in politics at Edinburgh.
He and the princess, 31, were first pictured together after Princess Eugenie's wedding.
Then in March they were pictured holding hands in New York before making an official appearance at the National Portrait Gallery Gala.
It is understood they met in September last year. Mr Mozzi has a child from a previous relationship - a toddler son called Wolfie.
