The tenant/domicile laws vary from state to state and sometimes from county to county.
Generally, by law, you must be given 30 days written notice to vacate any type of dwelling at which you have established residence and they can do nothing to force you out sooner without a court order. Did you receive a written notice?
If not, since your friend is being a prick, you could just "squat" an extra day and tell the cops - if they become involved - that the verbal agreement between you and him was to be out by the morning of the 1st of September but that he changed it to the morning of the 31st of August on you at the last minute. Without proof otherwise, cops will be extremely resistent to intervene without a court order because 1) its a civil dispute and 2) its only one extra day which is extremely minor.
All you need to show them is that you have established residence sufficient for the purposes of the law. Sufficient proof of residence is change of address on your driver's license, you receive mail there, were given a key to the door, and have lived there for the past 30 days.
There are even protections in some jurisdictions which permit a tenant to stay up to seven additional days even though they have not paid rent for those days and the tenant cannot be forced out without a court order.
But as I said, it varies from jurisdiction to jurisdiction. Generally speaking, if you follow my suggestion above, there is a very good chance you can get away with squatting an extra day and you can even call the cops if he attempts to remove you, starts harassing you, or attempts to physically remove your possessions from the apartment, and they will tell him that in the eyes of the law, you have as much right to be there as he does until a court says otherwise. I've seen landlords arrested for this kind of thing.
But you have to be the one to play it cool. Don't get into a confrontation with him, because the cops can take someone to jail of there is a disturbance. Be the first to call the cops if you think there is going to be trouble.