Quitting my job

Mind is already made up that i'm quitting. Just asking if this is a semi professional manner of doing so. I spoke to my general manager in March about leaving the company because I had academic and professional opportunities I wanted to achieve. I told him that the convo was basically my verbal notice and that I didn't have a date set. Left an immediate resignation letter with him last week. Should I call my immediate lead and inform him as well that I won't be returning? I've left every supervisor below the GM out of the loop of my departure. I dont know if he spoke to them or not.