All good advice. What hardware are you moving to/from? What are the specs of the different computers, and does the new one have the same license? What is the reason for the move?
Also, some backup programs like Acronis have the option to do a universal restore kind of option, where the new drivers can be injected into the old OS to ensure smoother booting/operation. All this said, I would recommend making a full backup first in case something goes wrong with the OS when you try to move it over.