Okay guys.
I have found the solution.
It was too easy to be true, but it is…
Basically, I have installed Perforce (which is proprietary, but free for 20 or less licenses - I have less. You may use any other SVN) source control, enabled it in Unreal Engine plugins, created a source-controlled repository, made a folder which is in sync with that source control and created my test project into that workspace. Then I clicked in Unreal “File → Source Control…” And configured the connections. Have to prevent you - interface changes slightly. New icons appear on content thumbnails (like it was an asterisk “not saved yet”, now some question marks and check marks appear and so on). New options appear in menus as well.
So, next what I will do, is configure that properly. Now it is enough for me that I have tried that working.
Note to developers: Guys, you are doing a fantastic work. I am sorry I didn’t find that option in documentation, although I have searched for it. Tutorials are focused on how do we create games using the Engine, but many users will appreciate a tutorial how to setup our workspace first.
Thanks to everybody, I got problem solved, consider closing the thread.