The decision follows a string of complaints about the contractor's performance which led to a local MEP calling for an independent inquiry.
Balfour was awarded the £150m, five-year contract in December 2012.
The new deal, which will also run for five years, will start in the second quarter of 2016.
The contract will cover construction and maintenance of highways, plus some work to bridges and flood defences.
Wiltshire is procuring on behalf of itself and Swindon Council, and the successful contractor will enter into separate contracts with each local authority.
Up to six bidders will be invited to tender for the contract following the pre-qualification process. Further information is on the official OJEU notice.