For the SSD I can't tell you exactly, but I recommend you check with the manufacturer of that unit for their free utility service tools. I expect that will include a means of erasing all data on it, or possibly over-writing all old data, just as I recommend for the HDD (below).
For the HDD, the safest method is a Zero-Fill. This process will write all zeros to EVERY Sector of the HDD so there is NO old data left anywhere. (As an aside, it also triggers an internal self-diagnostic and fixing tool.) When it is finished, the HDD is completely empty just like new from the factory. This process takes a long time (writes to every Sector), so just be patient.
You realize, of course, that this will destroy all data AND your Operating System. That is the whole point, right? When you have them both wiped, I suggest you do this sequence. DISCONNECT the HDD and leave installed and connected ONLY the SSD (I ASSUME that is to be your boot device with your OS on it) plus an optical drive IF that is where you will have your OS Install source. Set your BIOS to boot and run from the optical drive (if that's where you have an Install CD) or from a USB port (if that's where your OS Install stick is). Boot and run from there to install the OS on the SSD.
When the OS is running, remove the Install medium and shut down. Now install the HDD. Boot and go into BIOS SETUP immediately and set your machine to boot from the SSD. Remember to SAVE and EXIT to save this setting and let it boot up. When the system is running, go into Disk Management and find the empty HDD. RIGHT-click on it and tell it to Create a New Simple Volume on that drive, probably using all of its space unless you have other specific plans. IF the HDD is over 2 TB capacity, you will have to ensure it uses the new GPT Partitioning system, not the older MBR system. If you have the option, you do not need to do a Full Format because you've just done a thorough check of the unit. Just choose a Quick Format. When it's done, back out of Disk Management and reboot. Both storage systems should be ready to use.
Now you can start to re-Install all your application software.
The reason for that sequence is to defeat a Windows "feature" that can cause trouble. A normal Windows Install will look for a second storage device and, if one is available (e.g. your HDD) it will place on it in a small semi-hidden Partition a bunch of back-up copies of system files before doing the actual Install on the planned boot drive. The plan is that, if at some time in the future it starts to boot and finds corrupted system files on the boot drive, it will go find the backups on the other drive, copy over replacement good copies, then finish the boot. Self-fixing! Neat, eh? BUT on every boot event from now on it will check that those safe copies are there and if they are not (e.g., if you removed the HDD) it CANNOT BOOT without them! By NOT having the HDD installed when you Install Windows on the SSD you force it to put the spare backup copies on the SSD, too, so that they always will be found and you can always boot up as long as the SSD is working.