The couple, both 28, have chosen Westminster Abbey in the spring for their big day — and today said they were on "Cloud Nine".
The announcement was made at St James's Palace after a series of intense meetings between the royal household and Government officials.
St James's Palace sources ruled out any date before Tuesday April 26 because of Lent and Bank Holidays.
And aides urged them to balance their determination for a short engagement with hope for sunshine.
Happy Brits will be toasting the couple as the wedding means it will be a three-day working week.
Downing Street announced today workers will get an extra day off for the nuptials, which will follow the Easter Monday Bank Holiday on April 25.
Thousands of foreign tourists are set to flock to the capital for the wedding - which is expected to bring a massive boost to Britain's economy.
William and Kate were not in London as the details were confirmed.
He is on shift as an RAF search and rescue pilot in Anglesey, North Wales.
She is expected to return from Wales to her family home in Bucklebury, Berks, later today.
Royal tradition pointed towards a week day — Prince Charles wed Diana on Wednesday, July 29, 1981.
But Camilla married Charles on a Saturday because of a delay caused by the death of the Pope.
Westminster Abbey was the favourite venue to host the wedding after Kate was photographed leaving the historic place of worship in central London last week.
Sadly, the Abbey was also the venue of William's mother's funeral in September 1997.
Jamie Lowther-Pinkerton, private secretary to Prince William, said the couple chose Westminster Abbey for its "staggering beauty", 1,000-year Royal history and intimacy despite its size.
He said today: "The venue has long associations with the Royal family - it is in many ways the Royal family's church - and of course with Prince William personally.
"For Miss Middleton, the associations she has with the Abbey are quite simply the same as any British person would have for such a glorious and holy place."
By coincidence April 29 is St Catherine's Day, named after St Catherine of Siena, a nun who refused to marry and starved herself to death back in 1380.
She is the patron saint of fire prevention, bodily ills and sexual temptation and devoted herself to a life of fasting, prayer and service.
Catherine spent years nursing in hospitals, helping the poor and giving advice and support to people in prison and apparently even used to suck the pus out of her patients' wounds.
It was only on 5 May 1940 that Pope Pius XII named her a joint Patron Saint of Italy along with Saint Francis of Assisi.
Today, St James's Palace also announced that the wedding - including the costs of the church service, music, flowers, decorations, reception and honeymoon - will be paid for by the Royal family and the Middleton family.
Mr Lowther-Pinkerton said those planning the nuptials were very conscious of Britain's precarious finances.
He said: "All parties involved in the wedding, not least Prince William and Miss Middleton, want to ensure that a balance is struck between an enjoyable day and the current economic situation."
The aide added William and Kate were "completely over the moon" about their engagement.
He said: "I've never seen two happier people, which is absolutely fabulous to work in that sort of environment.
"They're on Cloud Nine, like any other newly-engaged couple.
"They're now getting stuck into organising their wedding. They are very much in charge of the arrangements for the big day.
"They're giving us and the Household office very firm direction indeed."
Prime Minister David Cameron said today: "The wedding of Kate and William will be a happy and momentous occasion.
"We want to mark the day as one of national celebration. A public holiday will ensure the most people possible will have a chance to celebrate on the day.
"The costs of the wedding itself will be met by the Royal Household, with Government meeting any wider security or transport related costs."
Mr Cameron was consulted on the date of the wedding, which will be less than a week before the local elections and expected referendum on voting reform on May 5 2011.
A senior Royal aide said: "He was very content with the selection of the date."
The couple are said to be keen on making their wedding a national celebration and a concert in Hyde Park to mark the occasion has been proposed.
The aide refused to confirm any further plans but said: "Their view on it would be, 'let's have a party'."
A Palace source today defended the length of time it has taken to arrange the crunch details and make them official.
He said: "It's still only a relatively short time since they got engaged — we're only on working day five.
"We've got to make sure everything is in place before we announce it to the world.
"Events like this do take time to get clearance on. There is no particular hold up."
The couple spent yesterday at their isolated farmhouse in Anglesey.
Stunning brunette Kate went to Waitrose in nearby Menai Bridge to stock up on food.
It is the first time she has been spotted in North Wales since the engagement was revealed.
Charles was congratulated on the forthcoming royal wedding as he chatted with cheering schoolchildren and their parents today.
Charles spent 15 minutes talking to a crowd of flag-waving youngsters outside Bradford's City Hall as he arrived for a visit.
Some of those who gathered in the freezing weather said they managed to bring up the subject of William and Kate.
Mandy Ervy said she told the Prince her 16-year-old daughter Laura was the lead singer with Beckfoot School band which accompanied the walkabout.
Mrs Ervy said: "I congratulated him on William and Kate and he said 'thank you'.
"I told him it was my daughter who was singing and he was very interested."
