The eastern end of Heathcote Road will be closed for six months from late next year while improvements are made to the bridge over Woronora River.
The state government has rejected calls to duplicate the narrow bridge, which has been the scene of many accidents over the years.
Instead, the lanes, shoulders and approaches will be widened.
There will continue to be just one lane in each direction on the bridge, which was built by the military in 1943.
Heathcote MP Lee Evans has previously stated his preference for the bridge to be duplicated, and Labor promised a scoping study for such a project at the 2019 state election.
A spokeswoman for Transport for NSW said on Thursday an investigation took place in 2019 into potential improvements, including widening the lanes and shoulders of the bridge and its approaches to improve safety.
"Widening the existing narrow lanes to standard lane and shoulder widths will significantly improve safety for motorists, especially larger vehicles," she said.
"Transport for NSW will close the bridge for at least six months to carry out the work uninterrupted to deliver these important safety improvements efficiently and reduce the impact of bridge and road closures to motorists in the longer term.
"A Review of Environmental Factors will be displayed later this year and early work on the bridge is expected to start in late 2021."
Transport for NSW is encouraging members of the community to complete a short online questionnaire, which will lead to them being updated on progression of the project.
The online questionnaire will be live until Friday June 5, 2020.
