Start making games. You need both the degree that you're almost finished with, AND a solid portfolio.

Yeah, start making games...

The games industry generally expects applicants to have some kind of past game development experience, no matter how well qualified they otherwise are. Typically this comes from 'hobby' work if you aren't already in the industry. Interestingly, this situation may begin to change as the supply of uber-keen applicants dries up to an ever expanding industry ... but I don't think it'd be wise to count on that happening soon.

So, you'd do well to have a demo, or demos. However, if I were you I'd start with simple projects that you can complete in a few days, and begin to get a feel for how to make interactive games work.
- Get something on the screen. You generally want as much control as you can in game programming, so you'll probably want to look into DirectX (or OpenGL, or a wrapper library over either) at some point.
- get something on the screen that you can control in real time, for example with the arrow keys. 2D is fine. Just get some interactivity in there!
- construct a solid game loop that updates game entities (such as the player) at a constant rate, irrespective of the speed of the PC.
- experiment with enemies, collision, graphics, 3D, maps, scrolling, whatever takes your fancy. There are plenty of resources on this site and elsewhere to help you.
- C++ is a tough language, but with a Java background you should be able to learn it as you go, and that will help as it's very common in the industry (as it's what things like DirectX work best with; C and C# also get some use, along with various scripting languages).

Let us know if you have any more questions.

Start with 2D games like Tetris or pacman. Learn how to render things on the screen, and how to get things moving due to keyboard input.

Next start adding more complexity into the games that you make. Soon enough you'll get the general idea of the flow of a game.

Then move onto 3D.