It does not have either of those accents. In one of the latest commercials he says he isn't British or Australian. I was searching and i found out he has a New Zealand accent.
While often mistaken for Australian, the GEICO gecko's accent is British. More precisely, southeast English (London or home counties). The British/Australian mix-up is used to comic effect in a...
It's definitely not Australian, it's English. There are lots of types of English accents, so it may not sound like the "typical" English accent you've heard before. Specifically, the lizard sounds...