The historic Grade-II listed structure closed for refurbishment in May 2013 and has been a bone of contention for more than half a decade as a series of setbacks.
The delays have also seen the budget rise from the original £6.9million allocated to £16.2million.
Work on the lifts is still underway, but transport chiefs have decided to open the tunnels to the public on Wednesday August 7, at 12pm.
Project manager Stuart Turnbull said: “It’s a relief to have the tunnels reopen after so many false dawns.
He added: “All the works, apart from the completion of the installation of the new inclined lifts which will replace two of the old escalators, are finished.
“Rather than keep the public waiting until the inclined lifts are operational, which we expect to be in mid to late September, we decided to open as early as possible given the long delay on the project and the high levels of anticipation amongst the public.
“We know that many people will want to come down and see the tunnels. Given the restrictions in place, we’d ask that those coming purely out of curiosity to avoid peak commuter times.”
Mr Turnbull thanked the public for their patience “during what has been a challenging time for everyone involved”.
He said: “We can now look to the future and enjoy again the unique experience of cycling or walking under the River Tyne between Howdon and Jarrow.”
The tunnels are owned by the Joint Transport Committee, which is the North East and North of Tyne combined authorities.
The project has been dogged by problems since the decision to renovate the grade-II listed structure was made a decade ago.
After closing in May 2013 for restoration work, the project was predicted to be finished by 2015.
But delays due to several contractors entering administration and the discovery of asbestos have seen the opening date pushed back several times.
When can I use the tunnels?
The tunnels will be open between 6am and 8pm, seven days a week until they become fully operational in September.
Continuing work on the installation of two inclined lifts means that the public must access and leave the tunnels via the vertical lifts. The public are advised that these can only hold two or three people with bicycles at a time.
What if I need to cross the river at night?
Since the tunnels closed in 2013, cyclists and pedestrians have been bussed across the Tyne between Jarrow and Howdon via the Tyne vehicle tunnels.
The shuttle bus will continue to operate until the end of August. The Night Service for shift workers will continue to operate as usual until the tunnels are fully open 24 hours a day in September.
What is the history of the tunnels?
The tunnels, which connect Jarrow and Howdon, cost £833,000 to build and opened in 1951 as part of the Festival of Britain.
At its peak, the structure saw an average of 20,000 people travel through every day – mainly workers travelling to shipyards on either side of the Tyne.
The tunnels, which are free to use, were the first purpose-built combined pedestrian and cyclist tunnels ever constructed in the UK.
The wooden-tread Waygood-Otis escalators were the longest in the world at the time of opening. The tunnels are 275m (900ft) in length and 40ft below the river bed at their deepest point.
What work has taken place during the closure?
The £16.2million refurbishment has had to meticulously match the original features of the structure because of its listed status.
It includes the replacement of two of the escalators with inclined lifts. The remaining escalators have been restored and kept in situ as exhibits but will not be operational.
All electrical and mechanical systems have been replaced. Modern CCTV and public address systems have been installed and are linked to the Control Room of TT2, which operates the Tyne vehicle tunnels.
Around 28,000 ceramic tiles replaced with 1250m2 of Formica panels and 1,900m of aluminium trims fitted, 3,630 paving flags have been lifted and relayed including 1978 new paving flags being manufactured.
The tunnels are linked to the National Cycle Network (Route 72).