If the IP and uplink speed does not change you can simply - stop tor at the old server - migrate the IP - migrate the tor config and the entire datadir - ensure the datadir is removed on the old server to avoid accidentally running more than one tor instance with the same key - ensure datadir permissions are set properly - start tor on the new server
Compared to only copying the key files, this will avoid tor assuming it is a new relay without prior history.
kind regards, nusenu