The royals' arrival coincides with what is expected to be a huge victory parade for the All Blacks in Auckland.
It is understood a parade in Christchurch will follow on Thursday and one in Wellington on Friday.
The royal couple's engagements have them in a different part of the country on those days. They are scheduled to visit Auckland later in the week.
An official statement said the majority of the seven-day visit will be based on a theme.
"Many of the tour's engagements reflect the themes of community, culture and conservation.
"For instance, the Prince and Duchess will have the opportunity to meet people in urban and rural areas ... and to learn how communities support one another."
Highlights include being welcomed on to Turangawaewae Marae in Ngaruawahia and watching a waka armada on the Waikato River - similar to an experience witnessed by Prince Harry earlier this year at Putiki Marae in Whanganui.
Unlike Prince Harry, however, it is not thought the royal couple will test their paddling skills.
Support for the royal family has increased in the last few years, particularly after the wedding of Prince William and the Duchess of Cambridge, and then the births of their children Prince George and Princess Charlotte.
In October, 2013 a Herald-DigiPoll survey found that 59.6 per cent of participants were against New Zealand moving away from the monarchy when the Queen died and 28.5 per cent supported the idea of becoming a republic.
However, a survey commissioned by the NZ Republic Inc in April showed 47 per cent of people wanted the next head of state to be a New Zealander - up from 44 per cent the previous year.
Royal arrival
Wednesday:
2pm: Arrive at Wellington Airport.
3.40pm: Official welcome at Government House.
4.10pm: Wreath-laying ceremony at National War Memorial Park.
6.15pm: State reception, Government House.