• The engaged couple face the massed ranks of the media inside St James's Palace
The prince is to marry his long-term girlfriend next year after he proposed last month, giving Miss Middleton his late mother Diana's engagement ring. It was, he said, "my way of making sure my mother didn't miss out on today".
In their first television interview together, the prince revealed how he had been carrying the ring in his rucksack for three weeks during the couple's recent holiday in Kenya before finally popping the question.
He said: "You hear a lot of horror stories about proposing and things going horribly wrong - it went really, really well, and I was really pleased she said yes."
His father, the Prince of Wales, welcomed news of the wedding, saying he was "thrilled, obviously" before joking: "They've been practising long enough."
Prince Harry said he was "delighted" his brother had popped the question, adding: "It means I get a sister, which I have always wanted."
The couple, both 28, met nine years ago at St Andrews University, where Miss Middleton caught the prince's eye while modelling lingerie during a student fashion show.
First Minister Alex Salmond insisted Scotland had played a key role in their flourishing romance, saying: "Of course, this was a match made in St Andrews, and everyone in Scotland will join with me in wishing the prince and Miss Middleton every happiness as they look forward to their wedding day and a long and fulfilling married life together."
Palace sources confirmed the couple may return to Scotland for their honeymoon after the wedding in London, with Balmoral or Prince Charles' Birkhall estate possible venues.
A royal spokeswoman said: "Prince William's grandmother does spend most of the summer months in Scotland, so that would certainly be under consideration."
Broadcasters cleared their schedules last night to show a TV interview with the couple, during which the prince revealed he had decided to ask Miss Middleton to marry him first, before asking her father for permission, in case he said no.
• In pictures: Prince William and Kate Middleton
• Scots connection: University 'matchmaking service' hails another success
• Around the world: Headlines from China to US
"I was torn between asking Kate's dad first and then the realisation that he might actually say 'no' dawned upon me. So I thought if I ask Kate first, then he can't really say no. So I did it that way round.
I managed to speak to Mike soon after it happened, really, and then it sort of happened from there.
"We've talked about today for a while, we've talked about this happening, so Kate wasn't in the dark at all when we were planning it for at least a year, if not longer. It was just finding the right time, and that's what most people say about couples; it's just about timing.
"I had my military career and I really wanted to concentrate on my flying and I couldn't have done this if I was still doing my training, so I've got that out of the way and Kate's in a good place in terms of work and where she wants to be, and we both just decided now was a really good time."Asked about the prince's late mother, Miss Middleton said: "Obviously I would have loved to have met her and she's obviously an inspirational woman to look up to."
She recalled that she "scuttled off" and went bright red when she first met the prince at St Andrews, admitting: "It did take a bit of time for us to get to know each other."
Before the interview was broadcast, Miss Middleton posed proudly with the dazzling oval, blue, 18-carat sapphire and diamond ring at a press conference in the state rooms of St James's Palace. Diana, Princess of Wales, who died in 1997, chose the elegant cluster ring after becoming engaged to Prince Charles in 1981.
Prince William said giving Miss Middleton his mother's engagement ring was "my way of making sure my mother didn't miss out on today and the excitement".
He added: "Of course, it's very special to me, and Kate's very special to me now as well, and it's only right the two are put together."
Paying tribute to his fiance as they posed together, he went on: "We both have the same sense of humour and we're both down to earth."
Miss Middleton, wearing a blue dress by label Issa, said joining the Royal Family was "daunting" but added: "Hopefully I'll take it in my stride."
She added: "We had spoken about our future and it just seems like a natural step for us to take. He's a true romantic and he's very supportive of me."
Asked about the proposal, she said: "It was very romantic, and it was very personal." William said it would remain a secret whether he got down on one knee.
As to why they decided to marry now after such a long relationship, the prince said: "I don't remember how many years it's been - forgetful memory. I also didn't realise it was a race, otherwise I probably would have been a lot quicker, but also the time is right now, we're both very, very happy, and I'm very glad that I have done it."
The Queen, during a reception at Windsor Castle, said: "It is brilliant news. It has taken them a very long time."
Staff at St Andrews University also welcomed news of the impending nuptials, and issued an invitation for them to return to the town to celebrate their wedding, or to mark the university's 600th anniversary next year.
Miss Middleton and Prince William, who is second in line to the throne, will marry in London next spring or summer. They will then live in north Wales, where he is serving with the RAF.
Ingrid Seward, author of the book William and Harry and an experienced royal watcher, said she expected part of the honeymoon to take place in Scotland, where the couple first met.
"It is not only a tradition among the Royal Family, but in Kate and William's case, Scotland is very much a big part of their love story. They love Balmoral. It is where their relationship grew and where they like to return to," she said.
Michael and Carole Middleton, Kate's parents, appeared outside their home in Berkshire - where police were on guard - shortly before 4pm yesterday to talk publicly about their daughter's relationship for the first time, saying they were "absolutely delighted and thrilled".
Mr Middleton said: "Catherine and Prince William have been going out together for quite a number of years. It's great for us because we have got to know him extremely well. We think he is wonderful. They make a lovely couple, they're great to be with, and we've had a lot of laughs together."
Prime Minister David Cameron said: "I am delighted to hear this wonderful news. I am sure the whole country will join Samantha and me in wishing them great joy in their life together."
Mr Cameron, who phoned William to offer his congratulations, said the prince was "extremely excited" and "thrilled".
Revealing that he slept outside Buckingham Palace on the night of the wedding of William's parents, Mr Cameron predicted next year's wedding would unite Britain. "I'm sure lots of people will want to celebrate in lots of different ways," he said.
Deputy Prime Minister Nick Clegg and his wife Miriam also sent their best wishes.
Labour leader Ed Miliband said: "I'm delighted for Prince William and Kate Middleton and send them my very best. The whole country will be wishing them every happiness."
Earl Spencer, who is Diana's brother and William's uncle, said: "It's wonderful news; very exciting. My family are all thrilled for them both."
The Duchess of Cornwall said news of the engagement was "absolutely wonderful".
No wedding date has been revealed, but Saturday, 13 August, is the bookies' favourite.
There were calls, however, for the wedding to be a less lavish affair than previous royal nuptials.
London mayor Boris Johnson said: "If they want a cut-price deal with a view of London landmarks, the ideal place would be City Hall. I'm not saying the wedding should be cut-price or bargain, but a cost-effective wedding in keeping with our cost-effective times."