There's Setup Assistant and Migration Assistant. The cleanest way to do it is Setup Assistant, but you only get that option once when you fire up a fresh install of OSX. If you're past that, you could reinstall OSX by booting with Command-R, or you could use Migration Assistant.
Setup/Migration Assistant instructions:
The cleanest way to do it is neither of those methods. The cleanest method to transfer files back is drag and drop them from the external harddrive, but since you have a Time Machine backup the best way is to go into the Time Machine interface and restore files from the external drive to your internal drive. Why was the harddrive wiped Lambrettalad? Were you experiencing problems with the OS?