Drivers will be able to use a five-mile stretch of the Aberdeen Western Peripheral Route (AWPR) between Tipperty and Balmedie, north of the city.
Further sections of the 36-mile road are due to open over the summer.
When complete, it will take through traffic away from Aberdeen's congested inner ring road.
Economy secretary Keith Brown announced in March that completion of the project would be delayed from spring until autumn following the collapse of Carillion, one of its contractors.
Only a short section between Tipperty and Foveran has opened, along with several junctions, to maintain access to other roads which cross it.
These started with Craibstone in September 2016.
On the latest new stretch, there will be access to the A90 between Foveran and Balmedie via new junctions at Newburgh and Tipperty.
A spokesperson for the Scottish Government agency, which is in charge of the project, said: "Traffic using the existing A90 between Balmedie and Foveran, and the new road’s southbound carriageway between Foveran and Tipperty, will be transferred onto the new Balmedie-Tipperty northbound carriageway.
"This change to road layout will enable the contractor to undertake the completion of the southbound carriageway and to connect the new sections of side road to the existing A90.
"It is yet another visible sign that works are progressing in this area on the new section of road, as well as on the existing A90."
Transport Scotland said the AWPR would reduce congestion, cut journey times, improve safety and lower pollution in Aberdeen city centre.
Next week’s section opening was welcomed by the IAM RoadSmart motoring group.
Neil Greig, its Scotland-based policy and research director, said: “At last some positive news from the AWPR.
“The opening of new sections like this, built to the most up-to-date standards, will give north east drivers a real first taste of the huge safety and journey time benefits waiting for them when the whole route finally opens.
“We hope that day is not delayed any further by any further construction or contract issues.”