Migrating an Office 2013 KMS host to another computer is similar to migrating an Office 2010 KMS host.

You can find the basics for Office KMS host migration at  Migrate an Office 2010 KMS host. For Office 2013, there is a new Microsoft Office 2013
KMS Host License Pack
and activation ID. And if the migrated Office 2013 KMS host will be running on Windows 8 or Windows Server 2012, you can also set
up and activate the KMS host by using the Windows UI.

To migrate an Office 2013 KMS host

1. Uninstall the Office 2013 KMS host key by running the following command:

cscript C:\windows\system32\slmgr.vbs /upk 2E28138A-847F-42BC-9752-61B03FFF33CD

2. Delete the record from the Domain Name System (DNS):

a. Open the DNS console.

b. Expand the _tcp node under domain.com.

c. Delete the _VLMCS record.

After you do this, the Office 2013 KMS host is uninstalled.

3. On the Microsoft Office 2013 KMS Host License Pack website, download and then run office2013volumelicensepack_en-us_x86.exe on the new server.
You are then prompted to enter the product key, and the Office 2013 KMS host will try to become activated. If the activation fails, do the following:

a. On the new server, re-install the product key for the Office 2013 KMS host by running the following command from an elevated prompt:
cscript C:\windows\system32\slmgr.vbs /ipk [ProductKey]

b. Activate the Office 2013 KMS host by running the following command from an elevated prompt:
cscript C:\windows\system32\slmgr.vbs /ato 2E28138A-847F-42BC-9752-61B03FFF33CD

Note: For a complete list of slmgr.vbs commands for Office KMS host activation, see Prepare and configure the Office KMS host.

4. After activation is complete, restart the Software Licensing Service and verify in the DNS that the record is created for the new KMS host server. For more information about how to configure DNS for the KMS host, see Understanding KMS.

5. To verify that the Office 2013 KMS host is configured correctly, check the KMS activation request count to see whether it is increasing. On the KMS host,
the current count is displayed when you run the following command:
cscript C:\windows\system32\slmgr.vbs /dlv 2E28138A-847F-42BC-9752-61B03FFF33CD

You can also check the Key Management Service log in the Applications and Services Logs folder, which is where activation requests from KMS clients are recorded, for the 12290 events. Each event displays the name of the computer and the time-stamp of the activation request.

To activate an Office 2013 KMS host that is running on Windows 8 or Windows Server 2012, you can also use the Windows UI. For more information, see Volume activation methods in Office 2013 and Volume Activation Overview