Balfour Beatty will construct a new bridge over the River Don, a new stretch of road linking it to the road network north of the Don, and realign and upgrade roads to the south of the river.
Cost of the scheme has gone up from an expected £15.5m to £18m as a result of recovery in the UK construction industry.
Convener Willie Young said: "The Third Don Crossing is a significant piece of infrastructure for Aberdeen and is a key project identified in Aberdeen's Strategic Infrastructure Plan.
"The bids for the project came in higher than anticipated, largely as a result of the economy picking up and the construction industry taking off again, but we are committed to the Third Don Crossing and have made provision for the additional costs."
The Third Don Crossing will see the construction of a new single carriageway link road between the Parkway/Whitestripes Road junction and the Tillydrone Avenue/St Machar Drive junctions, including the construction of the new bridge.
Construction will start later this year and the new bridge is due to be substantially completed and open to the public by late 2015.