Virtualmin makes upgrades and migrations as seamless as possible. The documentation below describes the process of upgrading to a new distribution, as well as migrating to a new server.
Migrations
Migrating To a New Server - How to migrate your Virtual Servers from an existing server to a new server.
Upgrades
On Ubuntu and Debian, it's possible to perform in-place upgrades of your distribution. The following documents describe how to perform those upgrades --
Ubuntu Upgrades
Upgrading Ubuntu 14.04 LTS to 16.04 LTS
Upgrading Ubuntu 12.04 LTS to 14.04 LTS
Upgrading Ubuntu 10.04 LTS to 12.04 LTS
Upgrading Ubuntu 8.04 LTS to 10.04 LTS
Debian Upgrades
Upgrading Debian Wheezy to Jessie