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The visit, rumoured for several months, will be the first New Zealand and Australian tour for Kate Middleton.
It's expected the couple will bring their son, Prince George, Royal Central reported. He will be nine months old and it will be the first time he has left England.
Prince William and Kate will spend between a week and 10 days on official engagements in both countries, beginning in New Zealand. But with rest days and travel, the entire trip will take the best part of a month, UK newspaper The Express reports.
Prince George is unlikely to accompany them on most of their public duties but aides anticipate there will be occasions in both countries when the infant will appear before the cameras.
Kensington Palace said details of the itinerary and exact dates "will be issued in due course".
Prime Minister John Key this morning confirmed the visit in April, saying he was "delighted" by the news.
"I am delighted New Zealand will have the opportunity to welcome the Duke and Duchess of Cambridge, who today confirmed they will visit Australia and New Zealand in April next year," Mr Key said in a statement.
"It's also anticipated Prince George will accompany his parents, but a decision hasn't been made on that yet and will be made in due course."
What do you think New Zealand should gift to Prince George? Send your ideas here.
Chloe Oldfield, vice-chairwoman of Monarchy NZ, said excitment was already building around the visit.
"I think we'll find we will have a real buzz and excitement that always seems to precede royal tours in New Zealand, like with Prince Charles and Camilla in 2012. There was large crowds that came out to meet them and lots of excitement, so I expect to see much of the same when Prince William and Catherine come next year," she said.
New Zealanders had followed the big events in the royal couple's lives, with the wedding and the birth of their first child, and would look forward to seeing them here, Ms Oldfield said.
"William, Catherine and George have all been quite a big part of New Zealand so I'm sure everyone will be pretty excited for Catherine and George's first time here.
"Prince William has quite an affection for New Zealand, he visited Christchurch and Pike River and seems to have a real affinity with New Zealand and we've quite a strong relationship I think, so he will be very keen to show his wife and new baby the country that he loves, and we're sure they will fall in love with it too."
Ms Oldfield said she would expect the royals to visit the main centres, especially Christchurch, where William could view the rebuild work which has taken place since he was last here in 2011.
"In terms of their interests, they have a keen interest in youth so I'm sure they would just love to meet lots of young people around the country, whether on a walk-about with the general public or a specific youth institution I'm not sure, but I wouldn't be surprised if that was one of the things they would ask to attend."
Coincidentally, Prince William, accompanied by his mother and father, Prince Charles and Diana, made his first visit to NZ when he was nine months old in April 1983.
Princess Diana had to ask special permission from the Queen to take her infant son on the six-week tour when he became the first royal baby to accompany his parents on an official overseas visit.
There was concern about the heir to the throne and the second in line travelling together on a plane in case it crashed.
Ms Oldfield said: "It will be pretty neat to recreate the scene of Prince William on the lawn of Government House, that would be pretty cool."
Prince William last visited New Zealand in March 2011, shortly after the Christchurch earthquake.
Check out the photos from his visit in the gallery here.
Before that he visited in 2010, representing the Queen at the opening of the Supreme Court Building in Wellington.
Prince William's visits to New Zealand:
Prince William played on the lawn of Auckland's Government House with her parents, Prince Charles and Princess Diana. Watch footage of that visit
2005: The Duke visited New Zealand privately when he followed the British Lions' rugby tour.
2010: Prince William represented The Queen at the opening of the Supreme Court building in Wellington, and also visited Auckland.
2011: The Duke of Cambridge last visited New Zealand to attend the Christchurch Earthquake Memorial Service and to visit the families of the Pike River miners.
2014: Prince William will bring his wife, Kate Middleton, and son Prince George to New Zealand for the first time.
Gallery: A collection of images from Prince William's NZ visits:
Image 1 of 15: Royal Tours: Prince Charles, Princess Diana and Prince William on the front lawn of Government House Auckland. 1983 New Zealand Woman's Weekly / NZH Archive. SUN 29Nov09 - NZH 16Jan10 - WGC 18Nov10 - BOP 18Nov10 - NAD 18Nov10 - NZH 11Jul11 -