Princess Eugenie cried when boyfriend Jack Brooksbank went down on one knee to ask for her hand in marriage, and she revealed the proposal was a "complete surprise" but the "perfect moment".
Eugenie's engagement to her long-term partner has been greeted with joy by her parents the Duke and Duchess of York, with Andrew summing up the feelings of the royal family with the words: "I'm absolutely overjoyed. I'm thrilled."
The Queen and Duke of Edinburgh also expressed their delight at the news, wishing their granddaughter and her fiance "all the best".
Eugenie, 27, and Mr Brooksbank, 31, got engaged in Nicaragua earlier this month during a private holiday, the palace revealed.
The princess began dating the brand ambassador of Casamigos Tequila about seven years ago after they met while skiing in the Swiss resort of Verbier.
Interviewed by the BBC's The One Show, with her fiance by her side, the couple said the proposal took place near an undisclosed lake.
The princess said: "The lake was so beautiful, the light was a special light I've never seen.
"I actually said, 'This is an incredible moment' and then he popped the question, which was really surprising even though we've been together seven years - a complete surprise.
"It was like this perfect moment, we couldn't be happier because we knew it was going to end up this way."
She added "I was over the moon, crying," and when asked if she saw the proposal coming, replied it was a "complete surprise".
The announcement has been marked by the release of a series of engagement photographs, with Eugenie proudly showing off her padparadscha sapphire and diamond engagement ring in pictures taken in Buckingham Palace's Picture Gallery.
Questioned about the Queen's involvement, Eugenie replied: "Granny actually knew right at the beginning, she was one of the very few people at the beginning, we left her this weekend and had a lovely time and she was very happy, as was my grandfather."
Eugenie and her fiance plan to marry this autumn in St George's Chapel at Windsor Castle - the same venue as Prince Harry and Meghan Markle's wedding in May - but Andrew said a date had yet to be chosen.
Speaking during a visit to the King's Lynn Innovation Centre, the duke said: "I'm absolutely overjoyed. I'm thrilled."
Of his future son-in-law, he said: "Jack is an absolutely outstanding young man and Eugenie and he have got to know each other over a number of years, and I'm really thrilled for them."
The duke said attention would turn to the planning of the wedding and "getting it all organised" but "we can't fix a date yet, we've got to look at everyone's diaries. It's a bit more complicated than that!"
He added: "But today it's their day. I'm just completely overjoyed for them and wish them every happiness."
In one picture released to mark the announcement Eugenie, wearing a colourful dress by Erdem and shoes by Jimmy Choo, and her fiance gaze into each other's eyes.
A Buckingham Palace spokesman said: "The Queen and Duke of Edinburgh are very pleased and wish the couple all the best."
In three tweets - which were retweeted by Andrew - Sarah, Duchess of York expressed her happiness at the news.
In one, she wrote: "Total joy!!" and included a picture of the couple overlaid with the words: "A total embrace of goodness and joy.
"We love Jack and I am so excited to have a son, a brother and a best friend. Eugenie is one of the finest people I know and so together it will be pure harmony."
Prime Minister Theresa May said of the announcement in a tweet: "My very best wishes to Princess Eugenie and Jack Brooksbank on their engagement - congratulations to the happy couple."
Mr Brooksbank's parents said in a short statement: "We could not be more delighted with the news of the engagement.
"We are completely over the moon and are very excited for them both."