I have a VPS server running Centos 6. Since this is quite old I would like to upgrade it to Fedora 25, preferrably without installing everything new from scratch. Is this possible somehow? While searching on the net I only found tutorials about migrating from Fedora to Centos, but not the other way round.
There is no official way to do this. You probably will have to reinstall. (You can take the opportunity to translate your configuration to something like Ansible, so you could re-provision in the event of a catastrophe — along with backups, of course.)
It might be possible to do an in-place upgrade using yum and dnf and a lot of work — but I'm quite sure this will be more work than reinstalling.