Prince William is to marry long-term girlfriend Kate Middleton next year, Clarence House has announced.
William, second in line to the throne, will marry in London next spring or summer and live in north Wales, where he is serving with the RAF.
"We are both very, very happy," the prince said. He had proposed on holiday in Kenya in October, giving his fiancee his mother's engagement ring.
Miss Middleton said joining the Royal Family was a "daunting prospect".
"Hopefully I'll take it in my stride," she added.
The couple, both 28, met at St Andrews University, Fife.
William said using Diana's ring was "my way of making sure my mother didn't miss out on today and the excitement".
Prince Charles said he was "thrilled, obviously" about the engagement, joking: "They've been practising long enough."
Kate Middleton's parents Michael and Carole said they were "absolutely delighted" and "thrilled" by the news.
Her father said: "We have got to know William really well, we all think he is wonderful and we are extremely fond of him.
"They make a lovely couple, are great fun to be with and we've had a lot of laughs together. We wish them every happiness for the future."
The royal engagement was announced in a brief statement released by Clarence House.
It said: "The Prince of Wales is delighted to announce the engagement of Prince William to Miss Catherine Middleton.
"The wedding will take place in the spring or summer of 2011, in London. Further details about the wedding day will be announced in due course.
"Prince William has informed the Queen and other close members of his family.
"Prince William has also sought the permission of Miss Middleton's father."
The Queen said she was "absolutely delighted" for both Prince William and Kate Middleton.
Prime Minister David Cameron said the engagement marked "a great day for our country" and wished the couple a long and happy life together.
He said he had received the news in a call from Buckingham Palace during a cabinet meeting, and it was greeted with "a great cheer" and "banging of the table" from fellow ministers.
He had slept overnight on the Mall ahead of Diana and Charles' wedding, he added.
Leader of the Labour party Ed Miliband said "the whole country will be wishing them every happiness".
Scotland's First Minister Alex Salmond said William and Kate's romance was "a match made in St Andrews" and everyone in Scotland would join him in wishing them well.
Welsh First Minister Carwyn Jones offered his congratulations, saying: "I'm very pleased to hear that they plan to begin their married life in north Wales."
The Countess of Wessex said the royal family was "absolutely thrilled and we all wish them all the luck and love in the world".
James Whittaker, who has reported on the Royal Family since the 1960s, said life as a princess will be "very very demanding".
Dickie Arbiter, the Queen's former press secretary, told the BBC: "She'll become a service wife.
"He'll have to do his statutory royal duty, his royal bit, but he will be very much a working helicopter pilot with RAF search and rescue for the next three years, and Kate will have to get used to living in North Wales, although I think she's pretty much used to it at the moment."
Meanwhile royal commentator Margaret Holder said she thought the marriage would give Prince William the warm, cosy, family life he wanted.
"What he's finding with the Middleton family is what he didn't have as a child and I think that's very good for him.
"I think this is going to be a very, very good and successful marriage. And I think this will take the monarchy through well into the 21st Century. I think Kate is very modern, she's very relevant."
Prince William and Kate Middleton both started out on the same history of art course at St Andrews in 2001, although William later switched to geography. For several years, they shared accommodation with friends.
Miss Middleton, who is six months older than William, was credited with persuading the prince to stay on as he struggled to adjust to university life during his first year.
They graduated in the same ceremony from St Andrews in 2005 and their families joined them for a celebratory lunch.
The couple's relationship was exposed in 2005 when they were photographed together on the Swiss ski slopes of Klosters.
They split briefly in 2007, but more recently Miss Middleton - who has no royal or aristocratic family connections - has been to several official events, heightening speculation of an engagement.
Miss Middleton is the eldest child of businessman Michael Middleton and former air hostess Carol.
She was raised in a modern five-bedroom detached house in the Berkshire village of Bucklebury and her family, who are self-made millionaires, run a mail order toy and party goods company.
The couple will marry in the year which would have marked the 30th anniversary of Prince William's parents' wedding.
The first interview with the couple will be aired on BBC News at 1900GMT. William and Kate - A Royal Engagement will be broadcast on BBC Two on Tuesday night at 1930 GMT.