Shropshire Council said it would be submitting a series of amendments to the application for the controversial road – with the main elements being major changes to plans for the bridge across the River Severn.
Shropshire Council's assistant director for infrastructure Steve Smith said that the bridge had been reduced from three lanes to two, with the removal of a 'creeper lane' for HGVs.
The bridge has also been shortened, along with a decision to use less concrete and steel cutting the cost significantly, as well as the carbon impact of the development, according to Mr Smith.
The saving will come from Shropshire Council's contribution to the project.
The overall cost is now £80.1m, and not £87m. The majority of the funding for the project has come from the Department for Transport, which has provided £54m, while the Marches Local Enterprise Partnership has given, £4.2m.
The council is expecting to have the application for the road considered by its planning committee before the end of the year.
The relief road, which would stretch for four miles from Churncote Roundabout to Battlefield, would effectively complete the ring road around Shrewsbury,
The proposals for the road have met with considerable criticism, with a significant environmental campaign arguing that it is an outdated solution, while also warning of fears that the costs could spiral, with Shropshire Council being responsible for any overspend.
Mr Smith rejected those suggestions, saying: "We have done a lot of work with our consultants and have a great deal of confidence in what the costs are at the moment.
"We have seen in the feedback about the costs rising to £130, we do not see that at all.
"We have a high level of confidence of the cost of this bid and we have been able to reduce that by that £7m."
Mr Smith said that the changes to the plans would cut the carbon impact of the project by 31 per cent – equivalent to 22,200 tonnes of carbon.
Councillor Steve Charmley, deputy leader of the council and and portfolio holder for physical infrastructure, highways and built housing, said he was committed to making the project happen.
He said: "It is a critical piece of infrastructure for Shrewsbury and the wider county. It has been 30 years in the making and now is very much the time to deliver it.
"We will grind to a halt in Shrewsbury and the hinterland around it if we do not get on with this. We have to build this and on my watch it will happen."
Councillor Charmley said the amendments to the plans address the comments submitted as part of the consultation, and added: "We recognise the Shrewsbury North West Relief Road would generate additional carbon in construction, and we looked at many different ways we can help reduce this. These changes do so by almost a third.
“This also takes no account of the much wider benefits that could come off the back of the scheme, such as freeing up road space in Shrewsbury to encourage more cycling and walking, and encourage people out of cars."