Smart cameras will be used to record number plates at strategically placed points along Harwood Terrace.
Residents have long complained to the council that the road is being used as a rat-run.
An experimental closure of the road last year found it was in fact being used as a cut through, mainly by out of borough drivers.
However, the council found that closing the road only led to a build up of traffic in other streets.
Drivers caught by the new cameras will be subject to a fine.