I'll assume you have a galaxy phone since you posted in the galaxy forum.

The only way to do this if you don't have the setting (a verizon phone?) under settings > -wi-fi

is do force stop the program that brings up the notification:
Attachment 54496

Every time my phone comes out of sleep a message pops up over my shortcuts telling me that it has connected to my router. This is something I DON'T need to be told, it gets in the way of the shortcuts and is very annoying. Does anyone know how to disable this?