It's almost that simple, but not quite: if you bought XP and installed it on your computer, then you have a transferable license. If it's an OEM version (i.e. preinstalled on the computer, or bought with a floppy drive or similar), then it's a non-transferable license.
Incidentally, if the hard drive in the old machine is as good as the drive in the new machine, you could just bang it in and let XP work things out: it will want to reboot about a bazillion times, but you may end up with a very simple change of computers.