The Queen is "absolutely delighted" at the news of Prince William and Kate Middleton's engagement, Buckingham Palace said today.
After months of speculation, the couple finally announced they will marry in London in spring or summer next year.
William and Miss Middleton, both 28, became engaged while on holiday in Kenya last month.
A Buckingham Palace spokeswoman said: "Both the Queen and the Duke of Edinburgh are absolutely delighted for them both."
After the wedding the couple will live in north Wales, where the Prince is serving as an RAF search and rescue helicopter pilot.
A spokeswoman for Prime Minister David Cameron said: "He is delighted with the good news. He sends the couple his very best."
Clarence House said in a statement: "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 and Miss Middleton became engaged in October during a private holiday in Kenya.
"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.
"Following the marriage, the couple will live in north Wales, where Prince William will continue to serve with the Royal Air Force."
A spokeswoman for Mr Cameron said: "He is delighted with the good news. He sends the couple his very best."
Deputy Prime Minister Nick Clegg and his wife Miriam also sent their best wishes.
"I am thrilled to hear the fantastic news of Prince William and Kate Middleton's engagement," Mr Clegg said.
"Miriam and I would like to send our very best wishes to the happy couple ahead of their big day."
And Labour leader Ed Miliband added: "I'm delighted for Prince William and Kate Middleton and send them my very best for their wedding.
"The whole country will be wishing them every happiness."
Miss Middleton, who comes from a wealthy middle class background, was born a commoner but is now in line to become Queen one day.
She met William at St Andrews University in 2001 while they were studying history of art.
Miss Middleton was credited with persuading the Prince to continue his studies when he considered quitting as he struggled to adjust to university life during his first year.
They moved into a shared house with two other friends in 2002 and reportedly became a couple around Christmas 2003.
The couple briefly split up in April 2007, reportedly because of the strain caused by William's military career, but they were secretly back together within weeks.
Miss Middleton's millionaire parents Michael and Carole, who is a former air hostess, run a mail-order business called Party Pieces which sells toys and party paraphernalia.
She was privately educated at the £15,000-a-year Marlborough College, where she was a keen netball and hockey player, and has two younger siblings, Pippa and James.
Miss Middleton was dubbed "Waity Katey" for her patience as she waited for the Prince to pop the question.
William is currently based at RAF Valley on Anglesey in north Wales, where he flies Sea King Mk3 search and rescue helicopters.
Mr Cameron, who phoned William to offer his congratulations, said the Prince was "extremely excited" and "thrilled" about his engagement.
Revealing that he slept on the Mall on the night of the wedding of William's parents, Prince Charles and Diana, Princess of Wales, the Prime Minister predicted that next year's Royal wedding would unite Britain.
"I'm sure lots of people will want to celebrate in lots of different ways," he said.
Earl Spencer, William's uncle and the brother of Diana said in a statement: "It's wonderful news. Very exciting. My family are all thrilled for them both."
William visited Afghanistan at the weekend to mark Remembrance Sunday with serving British troops.
Dozens of journalists, photographers and camera crews were outside Miss Middleton's family home on the edge of Bucklebury, Berkshire.
Police officers were on duty at the top of the private lane that leads to the Middletons' home.