Beatrice's younger sister, Princess Eugene, shared photos of the engagement on Instagram
Beatrice said on Twitter that she was "so excited" by the message.
The Duke and Duchess of York said, "We are thrilled that Beatrice and Edoardo have gotten married after watching their relationship develop with pride."
"We are the happy parents of a wonderful daughter who has found love and has found love and our companion to a fully devoted friend and loyal young man. We send them all the best wishes for a wonderful family future, "they added
" I know what a mother feels, so I have tears of joy, "added the Duchess
on Twitter .
"I'm so proud of this sensational news," she said.  "Andrew and I are simply the luckiest to ever have two great laws."
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The parents of Mr Mapelli, Nicky Williams-Ellis and Alessandro Mapelli Motsi said they were "truly delighted" with the 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 said.
" They share an incredibly strong and united bond, their marriage will only strengthen what is already wonderful relationships. "
Caption of images
Princess Beatrice and her fiancé Edoardo Mapelli Moti at the wedding of singer Eli Goulding last month
The BBC's Royal correspondent Johnny Diamond said he believed the couple had been together for about two years – and had been seen together in public on several occasions. He said things had "moved fairly quickly."
He said that Mr. Mapeli Motzi is a rich businessman who has a two-year-old son from a previous relationship.
Mr. Mapelli Motsi is the director of the Banda-owned
Beatrice's sister, Princess Eugene, married her long-time partner Jack Brooksbank at Windsor Castle in October 2018.
"I'm so happy for you dearest big sissy and dear Edo, "Princess Eugene said in an Instagram post, congratulating the couple.
"It's been a long time and you both have to be," she added.
Beatrice is the Queen and granddaughter of Edinburgh, and the cousin of the Duke of Cambridge and the Duke of Sussex.
Her parents, the Duke and Duchess of York, divorced in 1996. The Duke, Prince Andrew, is the third child of the Queen and Duke of Edinburgh
In addition to his royal engagements, Andrew serves as a Special Trade Government Representative until 2011, when his ties to disgraced financier Jeffrey Epstein forced him to retire.
Additional details about Beatrice's wedding will be announced in due time, her parents said.