Prince William has spoken of his and fiancee Kate Middleton's happiness, as the newly-engaged couple faced the cameras for the first time.
The couple, both 28, will marry next spring or summer after he proposed while on holiday in Kenya in October.
The prince said: "The timing is right now." His brother Harry said he would be gaining a sister.
William gave Kate his mother's engagement ring, saying: "It was right to put the two together."
Speaking as they stood arm-in-arm before photographers, and later as they gave a TV interview, Prince William said giving Kate his mother Diana's distinctive sapphire and diamond engagement ring was "my way of making sure my mother didn't miss out on today and the excitement".
He stressed that no-one was "trying to fill my mother's shoes". Miss Middleton paid tribute to the princess as an "inspirational woman".
She admitted joining the Royal Family was a "daunting prospect" but she added: "Hopefully I'll take it in my stride."
Ring 'in rucksack'
The Prince would not be drawn on whether he went down on one knee to propose, but, as the couple laughed, Miss Middleton said: "It was very romantic, and it was very personal."
The couple met while they were students at St Andrews University, Fife.
Speaking about their relatively long courtship, William said: "I didn't realise it was a race, otherwise I probably would have been a lot quicker.
"The time is right now. We're both very, very happy and I'm very glad that I have done it."
Miss Middleton added: "We have been going out a long time. We had spoken about our future and it just seemed the natural step for both of us."
Prince William told how he carried the ring around in the royal rucksack for about three weeks before he chose the right time to propose.
He said he knew he would be in trouble if he lost it, so he held onto it tightly.
And he revealed he asked Kate's father for her hand in marriage after he asked her.
"I thought if I ask Kate first then he can't really say no," he said.
Prince Harry's spokesman released a statement late on Tuesday after the prince had returned from flying training in Hampshire.
"I am delighted that my brother has popped the question. It means I get a sister, which I have always wanted," the statement read.
The couple will marry in London in 2011 and live in north Wales, where Prince William, second in line the throne, is serving with the RAF.
They said they hoped to have children. Miss Middleton said a close-knit family was important: "I hope we will be able to have a happy family ourselves.
Smiling, Prince William added: "I think we'll take it one step at a time. We'll sort of get over the marriage first and then maybe look at the kids. But obviously we want a family."
Earlier, Prince Charles said he was "thrilled, obviously", at the news, joking: "They've been practising long enough."
The Queen said she was "absolutely delighted" for them both.
Kate Middleton's parents Michael and Carole echoed those sentiments.
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."
Prime Minister David Cameron 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.
The royal engagement was announced in a brief statement released by Clarence House.
Prince William and Kate Middleton 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.
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.
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.
William and Kate - A Royal Engagement will be broadcast on BBC Two on Tuesday night at 2320 GMT in England, Scotland and Wales only.