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At 1100GMT Buckingham Palace made the engagement official.
Lord Maclean, the Lord Chancellor made the following statement at an investiture at the Palace: "It is with greatest pleasure that the Queen and the Duke of Edinburgh announce the betrothal of their beloved son the Prince of Wales to the Lady Diana Spencer, daughter of the Earl Spencer and the Honourable Mrs Shand Kydd."
Prince Charles proposed to Lady Diana three weeks ago at a private dinner at Buckingham Palace before she went to Australia.
He wanted her to use the trip to think over his proposal but she accepted immediately and he gave her a diamond and sapphire engagement ring.
Despite the intense public interest, they managed to keep their news a secret.
Lady Diana, who is 19, will leave her job as a kindergarten teacher and move out of her flat share in Kensington to live in Clarence House until the marriage.
The couple will then move to the Prince's house in Highgrove, Gloucestershire.
In a BBC interview, the 32-year-old Prince said he was "delighted and frankly amazed that Diana is prepared to take me on".
Looking shyly up through her long blond fringe and giggling occasionally, Lady Diana said she too was "delighted and thrilled, blissfully happy".
Asked how she would cope with a dramatic change to her life she said: "With Prince Charles beside me I cannot go wrong."
Tributes to the couple were made in both Houses of Parliament. The Prime Minister, Margaret Thatcher, said the news brought "great pleasure" to government and MPs.
They will be married in late July, but exactly when and where has yet to be decided.
Earl Spencer, Lady Diana's father, said he was also very happy for the couple.
Speaking outside Buckingham Palace with his wife Raine, daughter of novelist Barbara Cartland, he said his daughter had handled the pressures of constant media attention over the last six months very well.
"It will be easier now. She will be under some protection whereas before she had to face the music on her own," he said.
It was the wedding of the century and a national holiday was declared for the occasion on 29 July 1981.
Prince Charles and Lady Diana married in St Paul's Cathedral watched by 3,500 invited guests and an estimated 750 million people around the world on live television.
The sumptuous ivory taffeta and antique lace wedding dress was created by young British designers David and Elizabeth Emmanuel and had a 25-metre train.
Their first child, William, was born less than a year later on 21 June 1982.
After Prince Harry's birth on 15 September 1984 it was clear the fairytale marriage was falling apart.
The couple separated in 1993 and officially divorced in 1996.
Diana spoke publicly about her own and her husband's infidelities in a BBC Panorama documentary in November 1995.
Diana was stripped of the title of Her Royal Highness but was never far from the front pages of the tabloid newspapers.
She became actively involved with charities for children, the homeless, the disabled and those with HIV and AIDS.
She campaigned for a ban on the use and manufacture of landmines.
Her death in a car crash in Paris on 31 August 1997 shocked the world.
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