The answer is it depends. If you have an OEM copy of Windows, then there are no transfer rights and you'll have to get a new copy of Windows. If you have a retail copy, then you will want to be sure to prepare the OS for transfer by getting rid of the old drivers, but other than that you should be fine with little more than a reactivation.
And while it sounds like this is the plan, just to make sure, you can only use ONE copy of Windows on ONE system. Try and do more than that and one or both of them will be flagged as "non-genuine".