Prime Minister John Key greeted the couple before they were whisked off to receive a traditional Maori welcome in the capital.
William and Kate plan to spend the next few weeks enjoying a wine tasting at a local vineyard, meeting with The Lord of the Rings director Peter Jackson, going on a jet boat ride and visiting the city of Christchurch.
Prince William has visited New Zealand several times in the past, including shortly after a catastrophic earthquake struck Christchurch in 2011. However, it is Kate and George's first trip to the island nation.
The foreign tour is the family's first together, and comes 31 years since William made the same trip as a baby.
New Zealand's high commissioner to the U.K., Sir Lockwood Smith, said he spoke to Kate about visiting the Pacific nation previously.
"This was before Prince George was born, and she said, 'well, there's a little matter that I have to deal with first of course' and then she said, 'but I've got to say coming to New Zealand is top of my bucket list, I'd love to come and see New Zealand.'"