How to legally secure the rights to images?

Question

Design

The situation is very simple - I order a set of thematic sketches for my website from the artist. Accordingly, there is a risk tomorrow to see them on the sites of competitors. How to correctly formalize your rights to these products, so that in which case it is reasonable to demand their removal by third parties, or go to court?
How to fix the fact and date from the publication on your resource? It seems that Yandex had such a service.
Thanks in advance!