Basically no problem. You may have to activate on your new PC by telephone (i.e. call the activation centre, enter the code (received when slui.exe is executed) and then enter the code received on the PC). In the best case, you just have to enter the key and it works. As far as I know, there are no special Windows licences for this.

Small tip: Buying an OEM licence key on the internet is a lot cheaper (15 - 20.- for WIndows 10 Pro), but works exactly the same. These are the codes that the manufacturers use to activate their devices. Only the end customer pays himself silly.