As the royal couple's tour draws to a close, William praised his hosts for their legendary sporting prowess, flourishing arts and important role on the world stage.
William and Kate will stand shoulder to shoulder with Australians today when they join events marking Anzac day - a national day of remembrance for the nation's war dead, veterans and those still serving.
Speaking at a reception hosted by prime minister Tony Abbott at Parliament House in Canberra, William told guests: "Australia has a quality of life and a level of excellence that makes it a magnet: an enormously attractive place to live, trade, invest, and indeed just visit.
"The arts and sciences flourish; Australian sporting success is legendary; agriculture - from the traditional to the technologically most advanced - is hugely successful. This is a country that is in the front rank internationally.
"We have both seen all this for ourselves. Australia may be known as 'the Lucky Country', but often the harder you work, the luckier you get. Australians make their own luck.
"The distinct Aussie formula that has fashioned such a dynamic society is the source of admiration and envy around the world."
The royal couple's day began with a visit to the new national arboretum in Canberra, where they spoke to children about conservation projects.
Kate confessed she was sweltering in her bright green Catherine Walker coat-dress as she toured the attraction in the warm sunshine.
The innovative new national arboretum was created in an area of burnt-out pine forest following the devastating 2003 bushfires in Canberra.