Can I install Windows 7 on a HDD & then move that HDD to another PC?

[I WANT MY GIFS]

Can I install Windows 7 on a HDD & then move that HDD to another PC?

I have a OEM Product Key sticker for my old PC & my HDD died on that PC.
I plan to reinstall Windows 7 on that older PC with a new HDD I bought recently.

Thing is, I also have a newer PC I built.
Can I take out the HDD with the new instal of Windows 7 from my older PC & place it in my new built PC?

Will my new PC automatically then have Windows 7 on it or can that not work?

 

[AddRAM]

If you plan to re install windows on the older pc and use that key, you can`t use that key anywhere else. ( it`s OEM ) So you would have to buy a new windows license for the new pc.

Therefor it doesn`t make any sense to install windows on the new hard drive on the old pc, then move it. Just install windows 7 on the new hard drive in the new machine.

http://www.newegg.com/Operating-Systems/SubCategory/ID-368