A report reveals loose material has fallen off the Grade A-listed structure on several occasions over the past three years.
And an inspection found badly rusted steelwork and crumbling concrete.
A £22.3 million programme of repairs and refurbishment has been drawn up for the 120-year-old bridge, which carries the A7 over Market Street and Waverley station.
Work is scheduled to start this summer and be completed in autumn 2020.
But the report to the council’s transport and environment committee says it is a complex project, with work on the section of bridge over the railway potentially restricted to just two hours a night when trains are not running.
The report says: “Little maintenance work has been undertaken on the bridge other than in 1933 when steelwork was replaced near road level and in 1990 when the topside of the bridge was waterproofed and the decorative façade was painted.”
It says recent inspections showed it was in poor condition. “The bridge must be repaired to address health and safety concerns and safeguard the long-term use of this vital link to Edinburgh’s city centre.
“Over the past three years there have been a number of incidents of loose material falling from the underside and façade of the bridge.
“If repair work is not undertaken, the bridge will continue to deteriorate and it may be necessary to impose a weight restriction that could impact its usage by public transport and freight traffic.”
Work has already been undertaken to meet immediate safety issues and temporary netting has been installed to protect people passing underneath.
The report says most of the repairs and refurbishment can be carried out with “only occasional off-peak, overnight or weekend lane closures” affecting traffic on the bridge. It adds a temporary weight restriction may be needed, but this would not affect buses.
“Once the work is complete the bridge will be able to carry all normal traffic. This includes all vehicles up to a laden weight of 44 tonnes. This includes buses, trams and heavy goods vehicles.”
Councillors are also being offered the option to include additional improvements in the refurbishment, including widened and decluttered footpaths and carriageway resurfacing.
The report warns factors outside the contractors’ control, such as the weather and the time they are allowed to work above the rail line, could push the cost up.
And it says if the £22.3m repair programme is fully funded by borrowing, the total cost over a 20-year period would be £36.8m.
Transport and environment convener Councillor Lesley Macinnes said: “This historic bridge is a familiar and much-loved focal point in the city centre, and it’s clear that it requires some much-needed restoration. I am delighted that, thanks to prudent financial management, we will be able to progress with a series of repairs, ensuring the longevity of this iconic structure.”