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There is a nice example which seems to do exactly what I want - it’s even on the official documentation on GraphicsConfiguration.

But: If the left-most monitor is not the primary one - you should get negative X-coordinates - and that’s where the above example fails :(

After some trying I finally got this solution to it:

private Rectangle getVirtualScreenDimension() {
      Rectangle virtualBounds = new Rectangle();
      GraphicsEnvironment ge = GraphicsEnvironment
                        .getLocalGraphicsEnvironment();
      GraphicsDevice[] gs = ge.getScreenDevices();
      for (int j = 0; j < gs.length; j++) { 
          GraphicsDevice gd = gs[j];
          GraphicsConfiguration[] gc = gd.getConfigurations();
          for (int i=0; i < gc.length; i++) {
              virtualBounds = virtualBounds.union(
                                   gc[i].getBounds());
          }
      }
      Rectangle defaultBounds = ge.getDefaultScreenDevice()
                        .getDefaultConfiguration().getBounds();
      virtualBounds.x -= defaultBounds.x;
      virtualBounds.y -= defaultBounds.y; 
      return virtualBounds;
}