Yes, this is certainly possible. Basically you will have to wipe them both clean of previous data structures so they are like new empty HDD's. There may be a few wrinkles along the way, and you will have some options / choices to make. But the fact that you do not want to preserve anything on them make it easier.
The really thorough way to do this requires use of a utility and takes MANY hours, but if you're interested, here's how. You need a utility that will do a "Zero Fill" operation. If your drives are from WD, go to their website and download the Data Lifeguard - instructions etc. here:
If your drives are from Seagate, get their Seatools utility package.
In either case, I prefer the "for DOS" versions you burn to a bootable CD, because you can use them even without a functioning OS or HDD. But the "for Windows" versions may be fine for what you plan. If you HDD's are from some other maker, check their website for free utilities. Whatever you get, install one of your old HDD's at a time into your machine and run the utility to "Zero Fill" the unit. This operation takes a very long time because it means writing all zeroes to every sector of the HDD, plus checking them for reliability. But when it's done, the HDD has no old data, and you can proceed to the next steps. Moreover, almost all faulty sectors will have been found and substituted so the unit appears free of any faults - a good step in preparing to re-use an older drive. Once the fill operations have been completed, you can mount both units in your new machine and use Windows' Disk Management to Create a Partition and Format it (together these often are called Initializing the drive) on each drive. (A Quick Format, rather than Full, may be quite sufficient here after the Zero Fill, and takes much less time.) Then you can use them.
Now, if you're not interested in doing those long jobs, you can start by simply mounting both HDD's in your new machine. The trick here is that its BIOS may actually recognize that these disks are marked as members of a RAID1 array and try to use them as such. It is quite possible, however, that your system will tell you the RAID1 array if faulty, because it can't quite understand the data on it. No real problem here because you don't want that data, anyway. BUT you would need to look at the manual (probably a separate document from your mobo manual) for how your new machine manages RAID systems. Usually there is a specific key set you must hold down during the boot process to enter the RAID Management portion of BIOS. There you probably want to Break the RAID array (if there is one) so that the two drives are now recognized as separate non-RAID units, then exit out to let it finish booting. Once Windows is running, you can use Disk Management on each old HDD to Delete all its Partitions, then Create a new Partition and Format it (Initialize, again). The step I would recommend here, though, is that you choose for each old HDD that it does a Full Format (not Quick) so that Windows tests all the drive sectors to ensure reliability. This is NOT the same process as what the drive does during a Zero Fill operation, but it has a similar effect. AND it takes about the same LONG time to do.