Her parents announced on Thursday that the pair got engaged earlier this month in Italy and plan to marry in 2020.
The princess, 31, is ninth in line to the British throne, the granddaughter of Queen Elizabeth II, niece of Prince Charles and cousin to Princes William and Harry.
"We are extremely happy to be able to share the news of our recent engagement," the couple said in a statement, according to Efe news.
"We are both so excited to be embarking on this life adventure together and can't wait to be married".
Beatrice's parents, the Duke and Duchess of York, said: "We are thrilled that Beatrice and Edoardo have got engaged, having watched their relationship develop with pride.
Mozzi's parents Nikki Williams-Ellis and Alessandro Mapelli Mozzi said they were "truly delighted" by the news and added: "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."
Beatrice's mother Sarah Ferguson also congratulated the couple on Twitter.
"I know what a mother feels so I have tears of joy. I am so proud of this sensational news. Andrew and I are just the luckiest people ever to have two great sons in law," she wrote.
( With inputs from IANS )