Will transferring my old OS drive into my new PC affect the new OS Drive?

I have an old PC with Windows 10 OS on a SATA SSD. I'm building a new PC with the OS on a brand new drive but I want to transfer my old SSD to my new PC since there are files I want to keep.

Can I just unplug the SATA from the old PC and move it to the new one will will the OS clash when I boot? I've moved lots of hard drives from one PC to the other but this is the first time I'm doing this with a drive containing the OS. Please help!