I'm a student doing PhD in North America. I wish to keep open the possibility of settling down in Europe, Australia or Asia. By settling down I mean getting a tenured professorship in good universities at any of the above mentioned places.
I'm just starting out with my research and I'd like to know if I can do anything right now, i.e. during my PhD to boost my chances.
You should familiarize yourself with recruiting procedures in Europe/Asia/Australia and how they might be different from the US. while its early now, you should (when your research direction starts crystallizing) familiarize yourself with research in your area being done in institutions of interest, and identify people at conferences to chat with.
The main disadvantage you could face is a language barrier, local competition, and general lack of awareness because of distance. But except for the first, the others are less and less of a problem.
But at least for the first few years of your Phd just focus on finding interesting research problems to work on and do work that people will pay attention to. Thats much more important :)