The large services like GitHub and Bitbucket probably have articles on this, regarding the security aspect. The easiest way to get them on board should probably be to list the top reasons how git could save both time and money. For example the possibility to back-track, the strong collaboration features and such. People are always a little bit hesitant to something new to them but you can always showcase some of all the companies who use it (both large and small ones).
If security really is that much of an issue you can host it on your own servers using something like GitLab, so that shouldn't be an issue.