Speaking in Kilkenny this afternoon, the minister said letters will be sent to householders from local authorities reminding them of the penalties and interest relating to non-payment.
Full details of how the system will work will be announced early next week.
The Cabinet will discuss the issue on Tuesday.
More than 900,000 people have registered for the household charge, with €90m collected to date.
Mr Hogan said many people had expected it to be dropped or changed before the deadline date of a few weeks ago and they now realise what he had said all along, that it would not be.
The minister said he's very satisfied with the numbers that have paid in the past week in particular.
The estimate for the number of households who are due to pay the charge is between 1.6 and 1.8 million.
The 900,392 who have registered includes 14,655 people who have registered for waivers.