You could install a Windows 2012 R2 server and replace your existing KMS server. That would be great, but that's not a great solution for existing KMS customers. Instead, Microsoft has provided KB2885698 that will update KMS so that it accepts the new keys.
You can download it here: KB2885698 The down side is that this update does require a reboot.
Once you have applied the update, open an elevated command prompt and issue the following commands. NOTE: If the title of the command prompt doesn't have the word Administrator in it, then you aren't in an administrative command prompt.
Install the product key:
Activate the product key: