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."
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.
Prince William last visited New Zealand in March 2011, shortly after the Christchurch earthquake.
Before that he visited in 2010, representing the Queen at the opening of the Supreme Court Building in Wellington.
