When do I become a graduate student?
You're not really a student at your new institution until you have actually arrived and registered there.  At this point, it would appropriate to say something like:


  I will be a graduate student at Institute X with anticipated start date D


You can certainly update your CV to convey that information immediately.  

As for other sites, typically they allow you to list a number of positions with starting and ending dates.  If their system lets you list a start date in the future (I haven't tried that on the particular sites you mention), then that would be a clear enough communication of your current and anticipated status.  Otherwise, you can write the same sort of "anticipated start date" line in your free-text personal description.