Can I use an iphone bought in Europe in Australia?

I bought an iphone 4 in Europe in an apple store with no specific phone contract that came with the phone, I just used my old SIM card and I'm moving to Australia and I was wandering if it is still possible to use it in Australia with an Australian SIM card.

As long as it is not locked to a service provider and, from what you are saying it isn't so Yes.
Phones can always be unlocked anyway