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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.
The couple, who are both 28, became engaged in October during a private holiday in Kenya.
They began dating eight years ago while studying at St Andrews University in Fife, where they shared a house.
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."
'Delighted'
The Queen said she was "absolutely delighted" for both Prince William and Kate Middleton.
Prime Minister David Cameron's spokeswoman also said he was "delighted" and sent the couple his very best.
Ed Miliband said "the whole country will be wishing them every happiness".
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.
Stolen from the BBC http://www.bbc.co.uk/news/uk-11765422
He always said that he wanted to get married when he was 30 but that would mean the honeymoon clashing with the 2012 Olympics. Shame that, we could have entered them in the long jump.