Contractor Milestone Infrastructure secured an early contractor involvement deal two years ago following VolkerFitzpatrick’s completion of the first two phases (pictured in green above).
The council said the budget will now be increased from £31m to £47m.
Construction is expected to begin in Spring 2025 and be completed in 2027.
The final phase includes a new bridge over the River Hamble, a new roundabout junction with the A334 and a new access for Newhouse Farm.
Councillor Nick Adams-King, Leader of Hampshire County Council, said: “It’s important to provide transport infrastructure that creates the capacity to cope with additional traffic on the road network and minimise impacts on local communities.
“Completing this scheme will benefit residents and businesses in and around Botley village enormously, by reducing congestion, improving traffic capacity and, in turn, reducing noise and pollution in the village. To be able to agree the extra financial support required to fulfil our longstanding commitment to build the bypass is very positive.”