There are attorneys who specialize in landlord tenant disputes and you may want to confer with one of them before you do anything but, having made that disclaimer, since he is not on the lease, it seems to me that you are his landlord. You can evict him by giving a five day notice to get out (see http://www.supreme.state.az.us/info/brochures/evict.htm) and then take him to court and have him formally evicted. Grounds? Non-payment of rent as agreed. You can have an oral rental agreements. Now, here is what I worry about. Hopefully, you reviewed your lease with your own landlord and made sure that letting someone live on the premises who did not sign the lease is not grounds for your own eviction.
So, in short, yes I think you can file an eviction but you have to follow the right procedure. Just use this response as a start and see if there is a more civil, quiet way, to get this carpetbagger out of your home. Now, remember the disclaimer at the top of this response. It is worth the expense of having a 15 minute cosult with a landlord/tenant specialist and I recommend that you try and set one up.