The council will now go back to the drawing board to come-up with a simplified cable-stayed design.
Graham Construction and Vinci were the only two bidders left in the race after Ferrovial and Balfour Beatty dropped-out.
The job will now be re-tendered with a revised OJEU notice due later this year.
Concerns about construction risks on the job centred on the two independent curving bridge pylons.
They would have to have been built as huge unconnected post-tensioned structures rising 180m and 140m into the air.
Councillor Paul Watson, Leader of Sunderland City Council said: “While it is initially disappointing to learn that the unique design cannot be built within the budget available, we must now move forward positively towards our vision for a new Sunderland bridge, albeit by modifying our approach.
“The simplified design for the bridge will continue to embrace modern and tasteful design qualities, whilst maximising tested engineering technology and construction techniques.
“The fact that it is of cable-stayed design means that by its nature it will have a striking quality to it.
“It will sit within the same footprint and deliver on all of the benefits of the initial design, by reducing traffic congestion, improving connectivity and unlocking brownfield land – with its potential to increase growth, jobs and investment.
“What is most important is that we deliver a new crossing over the Wear.
“I have no doubt that the project team will quickly rise to this fresh challenge and I hope the city will embrace the new design once we are in a position to release further details.
“When the landmark design was first suggested, the city and the UK economy were in a very different place. Given the current economic climate we will not be seeking further funding, instead we must review our plans and work within our means.
“Sunderland undoubtedly needs a new bridge over the Wear to unlock underutilised land and improve infrastructure, attract further investment, to support the city long term economic growth and prosperity, as well as that of the wider North East region.
“Delivering a new bridge as soon as possible is the priority for us now and a simplified design approach is the smart and achievable solution.”
The revised bridge will transport two lanes of traffic in both directions, have dedicated cycleways and footpaths along its full length and retain the existing footprint.
