From 25 March, drivers turning right at junctions will have to give way to vehicles coming from the opposite direction that are turning left. At present, the driver turning right has priority.
At T-intersections, vehicles on the terminating road (the bottom of the T) will need to give way to all vehicles on the other road.
A road safety commentator, Clive Matthew-Wilson, says if there is any day in the motoring year when police should be out in force it is that day.
"The obvious thing to have done would have been not only to have had every available traffic policing car out there, but also every traffic policing car carrying large placards on all sides saying 'new intersection rules take place today'."
Police say the experience in Australia was that drivers were initially cautious and made allowances for each other, and they expect the same to happen here.