1. First of all it would have helped immensely if you had provided details re your new system and your precise objective in utilizing ("transferring") an "old HDD" from a "pre-built" system to a new system.
2. What do mean when you refer to a "pre-built" system? Was this a self-built generic type of PC or was it an OEM machine? Presumably the "old HDD" served as the boot drive (Win 8/8.1) in that system, right?
3. Re this "completely new rig"...is this an updating of the old PC (new motherboard, new CPU, various other components) or an entirely new system?
4. We'll assume that you plan to utilize the "old" HDD as the boot drive in the new system and NOT as a secondary drive. Presumably it contains a viable OS (hopefully Win 8.1 and NOT Win 8), i.e., it is non-defective, was bootable, and functioned problem-free in the old PC.
5. That being the case, as CountMike has pointed out, it's conceivable - even likely - that you can install that disk in your new build and it will boot & function just fine in the new system.
6. As a general proposition we have found the chances of a successful transfer increase when...
1. Both the old & new PCs are non-OEM machines, and,
2. Both PCs are either Intel-based or AMD-based systems.
Understand the above are not "hard & fast" rules. We've successfully transferred systems in spite of the above "criteria" not being met, especially in situations where the old PC is a OEM machine but the new PC is a non-OEM machine. But when all is said & done it's something of a crapshoot.
Obviously there are no guarantees that the transfer will be successful but it's worth a shot. There's little to lose since you always retain the option of fresh-installing the OS together with all your programs.
So if by undertaking this transfer you're fortunate enough to gain a bootable, functional system as a result, you will, of course have all your programs, personal data, etc. available without going through that rather onerous task of installing a new system.
Obviously you may have to install different drivers of one type or another in the new system but of course these will be available from your new motherboard's driver installation CD. And you may be pleasantly surprised at Windows (Microsoft's) ability to pick up & install whatever drivers are necessary for your new installation without user intervention.
Now another piece of advice...
IF YOU DO DECIDE TO UNDERTAKE THIS TRANSFER ATTEMPT WE STRONGLY SUGGEST THAT BEFORE DOING SO YOU CLONE THE CONTENTS OF THE DRIVE TO BE TRANSFERRED. SHOULD THE TRANSFER OPERATION FAIL (NOT AN UNUSUAL EVENT!), THE NEW SYSTEM MIGHT - REPEAT MIGHT - MODIFY THE DRIVE'S OS IN SUCH A FASHION THAT THE OLD DRIVE'S OS COULD BE ADVERSELY AFFECTED, RESULTING IN AN UNBOOTABLE OS IF & WHEN THE DRIVE IS RE:INSTALLED BACK IN THE OLD PC. WE HAVE EXPERIENCED THIS SITUATION IN RARE CASES. HOWEVER, THE DRIVE'S NON-OS DATA SHOULD NOT BE AFFECTED. AT LEAST WE'VE NEVER RUN INTO THAT SITUATION.
We've undertaken successful transfers of the type described many times and we nearly always undertake this option when circumstances permit, i.e. the above criteria I mentioned above are met.
And you do understand that you will probably need a new license for the new system so that it will be activated. But possibly not.
Let us know how the transfer went and provide some details about the two PCs involved.