The Queen's granddaughter will wed Mr Brooksbank in St George's Chapel in Windsor Castle in the autumn this year.
Buckingham Palace said Eugenie's parents, the Duke of York and his former wife Sarah Duchess of York, were delighted to announce the engagement.
The pair became engaged in Nicaragua earlier this month, the palace revealed.
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Eugenie, 27, began dating Mr Brooksbank around seven years ago after they met while skiing in the Swiss resort of Verbier.
The Stowe-educated socialite is the manager of Mayfair hotspot Mahiki.
Harry and Ms Markle are marrying in St George's Chapel in May.