First step, as VBorador2 said, is MAKE A BACKUP. Step 2 is check to be sure it's a good backup you can restore from. Step 3, if you're paranoid, is repeat steps 1 and 2 to another backup. Then go forward.
Maybe the most straightforward way to do this migration is to use utilities usually included with your RAID setup. Assuming you are using software RAID built into the mobo BIOS and chipset, you should have some RAID tools included in them, so read the manuals for this carefully. Those manuals probably are files on your C: drive, or maybe on a CD that came with your machine. If not, check the mobo manufacturer's website for it.
What you are looking for is two tools. One will undo a RAID1 set, converting the dual-disk RAID1 array you have into a single C: drive that is not in a RAID1 array, plus a second drive that is not in use. The other tool is a way to convert a single bootable HDD full of data, OS etc. into a 2-disk RAID1 array you can boot from.
So the plan is you un-make the RAID1 array you have, then boot from it to be sure you have a good stable system operating on one C: drive. There will also be a second unused drive that still has data on it. Your might be able to just leave that alone, but to be clean you might want to re-Format it.
Now you move both HDD's to the new system. You probably will have issues with getting your Windows OS to run on a new mobo with new hardware, and there are ways to handle that, too, which I won't deal with here. Anyway, you get to the point where your new system is working fine off one C: drive, and you still have a second empty drive.
Now you reboot and go into the RAID utilities and look for the one that allows you to add a second drive to a single-drive system and convert the two into a single RAID1 array. This is just what you did originally to establish you array, with the exception that this time you need it to keep all of the existing data and OS and make the array the boot device. The built-in tools should have a way to do that. When you're finished, you have your RAID1 array back in operation but all on the new machine.
AS I said, make your backups first and verify them. Then read all the RAID manual stuff to be sure you know where the tools are and how to use them BEFORE you start.
Added later: Hey, even better if you really want to understand, read all of the sticky by Somejoe7777 in the Storage / Hard Disk forum, second from the top.