RECOMMENDED: Make sure to take a complete backup of your data and save it to your computer or another server since all backups will be deleted before the migration! It's also a good idea to set a low TTL for your DNS records to limit the time it takes for DNS to updates, don't forget to set the TTL back after a day or 2 to reduce the number of DNS queries to your DNS servers.
Just go into Wyvern, select the server you want to migrate it to in the "Config" tab, and click the Change button. A ticket will be opened when the migration is completed and the new IP will be in the IPv4 tab.