They changed planes in Sydney to board a flight to Wellington.
The Duke of Cambridge could be seen holding a cuddly toy kangaroo for the eight-month-old prince, who was being carried by his mother.
The Duchess of Cambridge will realise a lifelong ambition when she arrives in New Zealand on Monday.
According to the New Zealand High Commissioner to London, Sir Lockwood Smith, right at the top of Kate's 'bucket list' is a visit to the Southern Hemisphere realm.
"I met the Duchess of Cambridge at a garden party at Buckingham Palace when she was pregnant with Prince George," he said.
"I said to her that I'd love her to come to New Zealand and she said: 'Well, there's a little matter I have to deal with first of course but I have to say coming to New Zealand is top of my bucket list.' And now she's finally making the trip."
Not only has Kate never visited New Zealand and Australia but it will be a first for son Prince George, who will likely one day be King of the two nations.
The tour will largely mirror that of the Prince and Princess of Wales' visit Down Under in 1983, when a nine-month-old Prince William conducted his first public crawl about.
Prince George, who is now eight months old, will arrive in Wellington, New Zealand after travelling long-haul for more that 24 hours.
To minimise the disruption to their son, William and Kate have decided to operate a hub tour in both countries, allowing them to return most evenings to be with George in Wellington and Sydney.
Excitement surrounding the royal party's arrival in Wellington for the start of the three-week tour is muted at best, although one local told Sky News: "We don't like to shout about it, and although the flags aren't out, we are quietly excited."
Two women who found it hard to conceal their excitement, however, are the owners of Wellington jewellery business Tory & Ko, who have been commissioned to design three pairs of earrings and one necklace for Kate for her stay in New Zealand.
"It's a complete honour and we are really blown away," Kirstin O'Brien told Sky News.
"She is the most perfect person to wear our jewellery because she is beautiful, sophisticated and she has that lovely accessibility about her,"
The Cambridge family will first visit the North Island, before heading to the South Island where they will spend a night away from Prince George.
All three, accompanied by their entourage including Prince George's newly appointed nanny, Maria Teresa Turrion Borrallo, will later travel to Sydney, Australia, for the second leg of their three week tour.