Jack, who is an entertainment manager, popped the question during the couple's holiday to Nicaragua in December.
The pair will follow in the footsteps of Prince Harry and Meghan Markle by marrying later this year at St George's Chapel in Windsor.
The news was posted online by the palace, with the official statement reading: 'The Duke and Duchess of York are delighted to announce the engagement of Princess Eugenie and Mr Jack Brooksbank.
'Her Royal Highness and Mr Brooksbank became engaged in Nicaragua earlier this month. The wedding will take place in the 9northern) Autumn of 2018 at St George's Chapel in Windsor, with further details to be announced in due coarse.'