Using my current copy of Win7 on a new PC build

I would like to take the copy of Win7 Ultimate I use now, and install it on a new PC build I will be getting in a couple of weeks. As soon as I can, I will get a new copy of Win8.1, but I am wondering if I can use the old OS on a new PC, before the 30 days (before activation) is up, and install the new OS on it before then, as an upgrade or full version? I'm assuming this can be done, as I...