while I agree with the above and the best option is to load windows afresh on the new PC, your other option is to just swap the drive and see what happens.
if it crashes, you're up for a fresh install anyway.
if it doesn't crash, Windows will detect the new hardware environment and install accordingly.
yes, this process may fail, but hey, it may work also. one of those suck it and see exercises.
if it does boot into Windows, the next hurdle is activation.
as stated previously, the Product Key is already assigned to the old PC, but the Windows Activation Servers are reasonably smart and can determine your eligibility themselves.
after booting, and once your connected to the web, Windows will try to auto activate, if it does, you passed all the MS authentications and are good to go.
if it doesn't, and your Windows version is not OEM, you can ring the MS automated help number and a robot will guide you through the process of re-activating on the new PC - I've done that hundreds of times, mind you not for a couple of years now but I doubt the process has changed that much.
they ask questions like, "press 1 to activate Office, press 2 to activate windows", "have you uninstalled Windows off the old PC?", "is the new PC the only one it will be on?", stuff like that. if you're being honest, you have nothing to fear, they fully understand old PC's die and licenses need to be transferred if allowed.