OPT to F1 conversion

[f1visaholder]

Hi, I've an MBA and i'm on OPT now. My OPT expires in June. I know there is a grace period of 2 months after the OPT expiration date. Can i join a school after the OPT expiration date and change my status to F1 in the Fall semester, say in August or September? Will i be out of status??? Does my class in Fall semester has to start before 60 days after my OPT expiration date?

your response on this is much appreciated

Thanks!!!