You can migrate your complete SolarWinds database with Help Desk Migration. The service is automated and possible to test for free. However, to set up a full data migration, you will have to pay. They allow migrating not only Tickets, but also Users, Groups, Ticket Notes, Ticket Attachments, Custom Fields, Tags, and Knowledge Base.
Of course, you just need to backup the database, install WHD on the new server, and restore the database. Pretty straight forward.
Solarwinds also has some documentation on it: Migrate Web Help Desk to another server - SolarWinds Worldwide, LLC. Help and Support
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