The bypass will remove traffic from Bedale, Aiskew and Leeming Bar and access to the Leeming Bar Industrial Estate will also be improved.
The scheme consists of a new 4.8km single carriageway road from the A684 north of Bedale to the A684 east of Leeming Bar, which links into Junction 51 of the A1(M).
The A684 is the principal east-west route between Northallerton, the county town of North Yorkshire, and the Yorkshire Dales.
The Department for Transport has granted final approval and is funding more than £29m towards the scheme, which is promoted by North Yorkshire County Council.
Work is scheduled to start shortly – a contractor is expected to be appointed imminently –with completion in May 2016.
Transport minister Baroness Kramer said: “The A684 scheme will provide significant environmental improvements to the communities bypassed. The very important local tourist market will benefit and the bypass will help support growth of the local economy.
“We are putting £29 million into this project because the government is serious about investing in the infrastructure the country needs to drive economic growth, both locally and nationally.”