Yes, you can. But you can only use the license on one machine at a time.
Once the license has been added to a certain computer it will bound there. The next time you register another machine with the same code it will give you an error.
But of course if you are not using the license on the old computer anymore. You can just give Microsoft a phone call (phone activation). Where someone will walk you through to some procedures and ask you some questions then release the license allowing you to reuse it on the new computer.
But phone activations are only available on weekdays. So you can try these steps, it might work:
Press Windows key + X
Click Command Prompt (Admin)
type: slmgr.vbs -upk
Enter
This will uninstall the product key from the computer. You can now use it on another machine.
Thank you for your help! Will the license work if I use it on a clean install rather than upgrade from Windows 7? – Timothy Wang – 2014-08-10T02:46:02.910
It should work either way. As long as the license is for that version and it isn't being used by another machine anymore. But you'll have to look more into that as I'm not too sure. I usually just install clean, haven't tried upgrading. – majidarif – 2014-08-10T07:40:55.430