Nows day the company will reply by verbal "accept" or "not accept".
It normally will reply instantly when you tender your resignation. In some case, some company will do DI (normal chatting) before they accept your resignation. They want to know the reason behind your resignation.
Just some extra info:
The resignation letter will start effect when you tender it to your superior, HR or your boss. They accept or not accept, you still can leave the company after the notice period (refer back to your confirmation letter for your resignation notice).