Hi
I just had to do that, myself.
My old boot drive was on my hard drive and I installed a new SSD and reinstalled my new Windows 10 install on that.
I was prepared to do tricks in the Bios but all I had to do was select the boot menu, tell it to boot to the SSD and it did.
I then opened Easy BCD to remove the old Windows install from the boot sequence.
What I found was that my old install didn't even show up.
After rebooting a couple of times to be sure, I removed the old Windows install and formatted the drive.
Don't remove the old install until you are sure that it boots to the new drive directly, without asking you which one.
Now on a different note, here are the instructions that the tech at Falcon NW gave to my about restarting the compute after installing on the new drive.
1. Disconnect the data cables from the other two drives when installing windows 8 and upgrading to windows 10 (so you are only working with a single drive) {I would also suggest switching the data cables on the back of the old drive and the back of the new one; the old drive is most likely connected to port 0 which is the best place for your operating system drive.}
2. After you are done installing Windows 10, turn the system off and reconnect the other drives. Then reboot but as you are rebooting tap the <Del> key to get into the BIOS.
Once in the BIOS if you go to the BOOT tab and find Hard Drive BBS Priorities, you can select the new SSD as the first boot option and disable all other boot options in this menu. (This makes it so the computer will only boot from this drive automatically, you have to put in a special key combination during the POST process to get it to boot from any other drive.)
As I said I didn't have to do this but you may.
Anyway, if you tell it to boot to the SSD and it does you can check or change the setup using EasyBCD.
Download EasyBCD - MajorGeeks
Remember that what ever drive you boot to will show up as drive C:\, so look at the drive size to make sure which one of the drives you are dealing with in EasyBCD.
Mike