Linton Bridge, over the River Wharfe in West Yorkshire, was damaged in the Christmas floods.
Emergency work has been undertaken but the cracked bridge between Linton and Collingham remains at risk of collapse, said Leeds City Council.
Work, which will cost £4.5m, is to start in July to put in place a river platform to work on the foundations.
Parts of the bridge dropped about 8in (20cm) after the floodwater undermined its foundations.
It has been shut since 27 December and the permanent repair works are expected to be completed by the summer of 2017.
More than 100 bridges were damaged by floods in West Yorkshire and a bridge partially collapsed in Tadcaster in North Yorkshire.
Councillor Richard Lewis said: "I think everyone now realises the challenge of repairing Linton Bridge is considerable and requires detailed and complex work, so is not something that can be done quickly."
The meeting also decided not to put a temporary footbridge in place due to cost and environmental impact.
A free shuttle bus service has been operating between Linton and Wetherby since January.

7 February 2017 Last updated at 07:41 GMT
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Andrew Sleat, 43, of Blackfold Road, Crawley, was also fined Â£300 at Crawley Magistrates' Court after he was convicted of drinking and driving.
About 20 people were evacuated from their homes after the crash in Ardingly High Street on 14 November.
Sleat's Ford Mondeo also damaged three cars in the village.

Jebb, 19, made 21 appearances for the Gunners' under-18 side last term and is an England Under-17s international.
McAllister, 25, missed most of pre-season after ankle surgery and is yet to feature for Shrewsbury this season.
"It's a good move for Macca and one which will hopefully see him play some games," said Town boss Micky Mellon.
"He is an experienced player and really needs to be playing games now that he is fully recovered from his operation."
Multimillion-pound repairs to a flood-hit bridge have been approved by senior councillors.
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