The admin option will be coming soon. In the mean time you can do it manually like this: (assuming it's a 'direct' file server)
- Set the server into 'Read Only' mode via the admin area, file server settings.
- Sync all files between both servers using rsync or similar. Include the script files.
- Make sure the storage path is correct for the new server in the admin area, file server settings.
- If you've the urls pointing directly to the file server, repoint the domain to the new server.
- Once propagated you can take the old server offline.
- Take out of 'Read Only' mode if needed.