The contractor beat rival bids from Galliford Try, Graham Interserve, Boot and Balfour Beatty with an £11m bid for the Tinsley Link road project.
Construction will start in January 2014 on the 800m long stretch of road that will be built under the Tinsley Motorway Viaduct.
The complex civils project was initially estimated to cost up to £24m to build. It will also cross tram tracks and bridge an existing rail freight line, as well as going over the River Don in two locations, and includes the design and construction of a substantial piled reinforced earth embankment and also traffic management.
When finished in Autumn 2015, the road will by-pass Junction 34 of the M1 motorway and provide an alternate route for all vehicles. It would also include priority measures for public transport.
The new link will help to unlock economic development in the Lower Don Valley by funding a high frequency bus service from Rotherham to Sheffield and increasing capacity for local traffic around junction 34 of the M1.