The queen said she is "absolutely delighted" for the couple, Buckingham Palace said today.
Like the queen, Middletons' parents, Michael and Carole Middleton, said they too were "absolutely delighted" by the announcement.
"As you know Catherine and Prince William have been going out together for quite a number of years which is great for us because we got to know William really well. We all think he's wonderful and we're extremely fond of him," Michael Middleton told reporters today. "We wish them every happiness for the future."
William admitted in an interview that he popped the question before asking for Michael Middleton's permission.
"I was torn between asking Kate's dad first and then the realization that he might actually say no," William told ITV. "I thought, if I ask Kate first, then he can't really say no, so I did it that way round and managed to speak to Mike sort of soon after."
The announcement came to the elation of Britons, many of whom viewed the engagement as a seemingly inevitable, yet unreachable moment. Within just 25 minutes of the announcement's post on the royal Facebook page, more than 1,400 people "liked" the news.
"It's about time! Congrats," one commenter wrote, a sentiment echoed by hundreds of others.
The wedding will take place in the spring or summer next year in London, the statement said.
British Prime Minister David Cameron said today he congratulated William on the engagement.
"He was obviously extremely excited about the news and thrilled about what lies in store," Cameron told reporters.
The couple plans to live in north Wales, where Prince William will continue his service in the Royal Air Force, the statement said.
While the announcement was "welcome words" for Middleton, royal expert and Newsweek editor-in-chief Tina Brown said it was made after a shaky start.
"This wedding was originally going to be announced in June, but there was a tussle," Brown said. According to her, the royal family disagreed about several details about the wedding even down to how the announcement would be made.
At one point, William called the wedding off, Brown said. But after all was settled, William's father, Charles the Prince of Wales, was the one to make the announcement through royal officials.
In a documentary aired on Britain's Sky News last month, William played coy about the deluge of engagement rumors the couple suffered for years.
"There is always speculation," he said. "But, you know, it comes with the job, so get on with it."
At the time, British bookmakers were so confident the wedding would happen in 2011 that they stopped taking bets -- a popular pastime for royal watchers and gossip-lovers.
Middleton comes from a family of commoners. Her father was a pilot and mother a flight attendant. She has been the target of some criticism because she does not have a regular job of her own, aside from sporadic work in fashion.
Middleton told ITV that she ignored much of what's said about her in the media. "I'm working hard and pulling my weight. Everyone can see. ... That's that matters to me. You have to be yourself. That's how I've stuck by."
William and Kate broke up briefly in 2007 but were back together within months.
Prince William is second in line for the throne, after his father Charles, Prince of Wales. Prince William's mother was Diana, Princess of Wales, who died in an auto accident in 1997.
ABC News' Nick Watt, Sarah Netter, Jason Volack and Bradley Blackburn contributed to this report.