The 31-year-old daughter of Prince Andrew and Sarah, Duchess of York, got engaged to the 34-year-old property tycoon in Italy earlier this month.
The princess, who is ninth in line to the throne, will marry Mr Mapelli Mozzi next year.
"We are both so excited to be embarking on this life adventure together," the pair said in a statement.
"We share so many similar interests and values, and we know that this will stand us in great stead for the years ahead, full of love and happiness," they added.
The Duke and Duchess of York are delighted to announce the engagement of Princess Beatrice to Mr Edoardo Mapelli Mozzi. Read the full announcement here: https://t.co/E7VRBC7H96 pic.twitter.com/7sSIVy8Kmj— The Royal Family (@RoyalFamily) September 26, 2019
Beatrice and Edo (as he is reportedly known) began dating in 2018 and made their first public appearance together when they attended the Portrait Gala in March of this year.
In true royal tradition, the couple won't have a long engagement. Usually, royal nuptials happen less than a year after the engagement announcement, and the statement confirmed that the wedding will take place sometime in 2020.
Beatrice's sister, Princess Eugenie, married her long-term partner Jack Brooksbank at Windsor Castle in October 2018.
"I'm so happy for you my dearest big sissy and dear Edo," she said in an Instagram post congratulating the pair.
"It's been a long time coming and you two are meant to be," Eugenie added.
The Duke and Duchess of York said: "We are thrilled that Beatrice and Edoardo have got engaged, having watched their relationship develop with pride."
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 pic.twitter.com/WIhe9eamrF— Sarah Ferguson (@SarahTheDuchess) September 26, 2019
"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," they added.
"I know what a mother feels so I have tears of joy," the duchess added on Twitter.
"Andrew and I are just the luckiest people ever to have two great sons in law."