William proposed during a holiday in Kenya last month after asking Kate’s father for his daughter’s hand.
The couple, who are both 28, have been together for a marathon eight years. Kate had been dubbed ‘Waity Katy’ amid criticism she was hanging on for a proposal but now her wait is finally over.
They were due to appear in public later on Tuesday, when the Princess-in-waiting was expected to show off her engagement ring and the first ever interview with the pair was being broadcast on Tuesday night.
David Cameron said William is ‘extremely excited’ and ‘thrilled’ as he appeared outside No10 to welcome the news.
Their wedding will be the biggest royal event since the wedding of Prince Charles and Diana in 1981.
It is hoped the ceremony will give a huge boost to the nation and the economy as crippling public sector spending cuts hit home.
Bookies have made August 13th the early favourite for the wedding date and it is likely to take place at Westminster Abbey.
It is claimed personnel at the Abbey have already been contacted about a royal wedding in the second week of August, although St Paul’s and Windsor Castle are other potential venues.
The engagement was announced simultaneously on Facebook and Twitter, coming days after the Queen signed up to the social networking site.
In a full statement, Clarence House 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 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 Buckingham Palace spokesman said: ‘Both the Queen and the Duke of Edinburgh are absolutely delighted for them both.’
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.’
David Cameron and Labour leader Ed Miliband both said they were ‘delighted’ for the couple.
The Prime Minister was told of the engagement during the Cabinet meeting on Tuesday morning and relayed it to ministers.
He emerged from No10 just before 1pm to express his joy at the announcement and revealed he had just spoken to the Prince.
‘I spoke to Prince William a few moments ago and passed on my congratulations. He was obviously extremely excited about the news and thrilled about what lies in store. It was wonderful to have that word with him and pass on my best wishes,’ he said.
Cameron added: ‘This is incredibly exciting news and I am sure the whole country will want to pass on their congratulations.’
Recounting how he was handed a note with the news during the Cabinet meeting, he said: ‘There was a great cheer that went up and a banging on the table.’
He said: ‘It’s great to have a piece of unadulterated good news that everyone can celebrate and be happy for them. I am sure it will be something when the country will come together. I remember when William’s mother got married, I slept on the Mall that night and joined in the celebrations. I’m sure lots of people will want to celebrate in lots of different ways.’
He added: ‘As well as this being a great moment for national celebration, I think we also have to remember that this is two young people who love each other who have made this announcement, who are looking forward to their wedding, and we must give them plenty of space to think about the future and what they are about to do.’
Kate’s security detail will now be instantly upgraded to give her round-the-clock protection.
Earlier this month, the Daily Mail exclusively revealed how her parents were guests at a private shooting party on the Queen’s Scottish estate.
The move was seen as highly symbolic and an indication that the middle-class Middleton family were now firmly being welcomed into the royal fold.
It is now clear that Kate and William were already engaged at the time of the visit to Birkhall, Prince Charles’ private residence on the Balmoral estate.
The invitation to Middleton, a former airline despatcher, and ex-air hostess Carole shows the Royal Family were keen to start off on the right foot as Kate moves to becoming a princess.
She and William first met at St Andrews University where they were both studying history of art and lived close to each other in the halls of residence.
It was at a charity fashion show in March 2002, when Kate modelled a sheer black lace dress, that she was said to have first turned the Prince’s head.
They moved in together with friends in 2002 but are not thought to have become a proper item until around Christmas 2003.
Their romance was exposed on a skiing holiday in Klosters in 2004 but William famously proclaimed: ‘I don’t want to get married until I’m at least 28 or maybe 30.’
They split up in April 2007 as William became increasingly involved in his career in the Armed Forces but were secretly united within weeks.
In the past few months, the pair have been ‘road-testing’ married life on Anglesey, in Wales – although officially Kate was still living at her parents.
There was a significant change last month when they were seen together in public at a friend’s wedding.
They notably walked in to the ceremony in Gloucestershire on October 23 together, with Kate beaming.
Usually, they always arrived at events separately to avoid being pictured together.
The last time Kate was seen was in July and it is thought she had been kept in the background ahead of the engagement announcement. The Daily Mail