LibGDX jars not part of the generated project and instead deep in .gradle folder

So I’m trying to lay the foundation for a small school project for my Game Design class. I said that we could use LibGDX for Android compatibility, and now I’m in charge of setting it up of course. The problem is that I just cannot fathom what I’m supposed to do to get this project pushed completely to GitHub so we can actually collaborate. The LibGDX project creator generated dependencies like this:

Is there any way I can make LibGDX generate sane library dependencies or should I just clone my harddrive and mail it to my teammates?

When you generated your LibGDX project with the setup app provided on the LibGDX download page and imported the generated project as Gradle project in Eclipse, then everything is setup properly. Yes, you do see references to absolute file system paths in your Eclipse setting files, but those you will never commit to Git.
Instead, everyone of you would just once import the LibGDX project as Gradle project in whatever IDE they prefer to use. During that process, all needed dependencies are downloaded as jar files and the IDE is configured with file system paths valid on that host system only. For Android projects I’d also REALLY use Android Studio / IntelliJ instead.
You’ll see that the setup app even created proper .gitignore files which will prevent anyone of you from committing any IDE settings files, compiled class files or (God forbid) jar files to Git.
You should be fine to simply git add -A && git commit -m "Create the start of our awesome LibGDX project".