The limit along Princess Street in Chase Terrace will be cut from 30mph to 20mph.
As part of a raft of safety measures being introduced, parking restrictions will also be put in place along some sections of the road, mainly at junctions with other routes.
County and district councillor Sue Woodward said there had been long-running problems along Princess Street over the years with speeding drivers and people parking inappropriately outside homes.
Those were the main reasons why she joined forces with fellow Chase Terrace Councillor Eric Drinkwater to push through the changes.
Councillor Woodward said today: "There have been long-standing traffic management concerns and problems along Princess Street.
"It has been plagued with inappropriate parking outside of homes and also speeding drivers.
"We want to make Princess Street a 20mph road."
Councillor Woodward and Councillor Drinkwater have held two public meetings to discuss the move with residents.
Letters have now been sent out to homes in the area telling them about the planned changes that are about to be brought in. A period of formal consultation has been launched and will take place over the next few weeks, although residents have mainly been in favour of the speed limit reduction.
Councillor Woodward added: "There are no simple solutions to this. We think these measures will bring some respite for the residents though.
"There have been problems along this stretch of road for over 10 years. In the last two or three years me and Eric have worked together on this scheme.
"We've tried to work out some sort of plan for the whole of that area. I'm chuffed we are coming to the formal consultation stage. I'd urge residents to respond to the consultation."
Princess Street over the years has had various traffic calming measures introduced including speed bumps and Lorne Street and Eastgate Street, which both lead off the road, have also been changed into a one-way system.