Wozniak waited overnight at an Apple store in Queensland and bought two phones, one white, one black, the Los Angeles Times reported.
"I went in thinking I liked the black better, but now I'm thinking I like the white better," he said.
Wozniak, who co-founded Apple Computer with Steve Jobs in 1976, is in Australia for business and to attend a concert.
Demand for the latest Apple phone has been unprecedented, the company said.
Some people in Sydney waited in line three days to get the phone. In Hong Kong, customers were escorted into stores one at a time to chants of "iPhone5, iPhone5" by sales clerks.
People waited in darkness outside stores in the United States to buy the phone.
More than 2 million pre-orders were placed in the first 24 hours after availability of the new phone was revealed, twice as many as the earlier version.
As many as 10 million of the new phones may be sold by the end of September, analysts predict.
Descriptions of the new device evoke those of superheroes: It's taller, faster, and slimmer. It has a bigger screen.
And it's already controversial.
Rival Samsung said Friday it would include the iPhone 5 in its long-running patent infringement suit against Apple.