Works by main contractor Pyeroy will also take much longer than the original timescale after significant areas of corrosion were discovered on the Grade II structure.
Pyeroy started repairs on the 80-year-old bridge in July with work scheduled to be completed by next month.
The completion date has now been put back to next Spring.
But motorists should be able to use the A1032 which runs across the bridge by the end of this month after Stockton Council changed the way works are carried-out.
The amended project will see a large tunnel style scaffold constructed which will allow the A1032 to fully re-open so motorists can use the road while the remaining repairs and painting take place.
Stockton Council’s Cabinet Member for Regeneration and Transport, Councillor Mike Smith, said: “We know how well used the A1032 is and appreciate the frustration its closure has caused so we are working hard to construct the scaffold tunnel as soon as possible.
“Once it is complete, motorists will be able to use the road as usual.
“The damage that has been found is a lot worse than we anticipated so we have reacted decisively to change the repair and painting programme.
“It would be counter-productive to carry out a quick ‘patching-up’ exercise as this would result in us having to re-close the bridge to carry out more extensive works in a couple of years.
“We have a duty to maintain this iconic structure and it is important that we repair it properly now to prevent even more disruption in future.
“We carefully plan our finances so we have sufficient contingency reserves to cope with circumstances like this.
“Consequently, we have committed £4.1 million to pay for the revised programme so that motorists can use the road while the works take place.”