The 27-year-old got engaged to the 31-year-old nightclub manager earlier this month on a trip to Nicaragua, Buckingham Palace has told.
The Queen's granddaughter told BBC: 'I was over the moon. [It was a] complete surprise. But it was the perfect moment, we couldn't be happier.'
Mr Brooksbank said: 'It was amazing.'
The portraits were taken in the portrait gallery of Buckingham Palace, and give the first glimpse of the royal's new sparkler.
The ring features diamonds with a coloured centre stone.
Eugenie further told how Queen Elizabeth and Prince Philip were delighted to hear the news.
'Granny actually knew right at the beginning [of the engagement]. She was very happy as was my grandfather,' she told the BBC.
The princess' mother was also delighted by the news, taking to her Instagram account almost immediatley after the news was shared.
Sarah 'Fergie' Ferguson wrote: '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.'
The two are set to wed in Autumn (September - December) at St George's Chapel in Windsor Castle - the same location Prince Harry and Meghan Markle are set to marry in May.