Shropshire Council's cabinet member for highways, Steve Davenport, was given the assurance during a visit to London this week.
Councillor Davenport said: "After much lobbying of ministers they have agreed to fund the road. He said that a formal announcement regarding this will be made in the first week of February.
"I am absolutely delighted with this. It has been talked about for the last 40 years and it really ramped up in the last 18 months.
"Shrewsbury's MP, Daniel Kawczynski, has been amazing, not only in lobbying but also in getting me in front of ministers so that I could put a business case forward to the Government.
"The North West Relief Road is going to bring a lot to the town. It will take traffic out of the town which is really needed.
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"We have got to manage that and see emissions fall. It is going to attract business to Shropshire and Shrewsbury. All the villages and rural roads which have been put under pressure will also benefit. It is a win-win and there will be future growth for Shrewsbury."