When work started on phase 1 of the new mile-long dual carriageway in Aylesbury the project was expected to cost £114m.
Being built in stages, the road is set to open at the end of 2026 – with the second phase to be completed by December 2024.
Galliford Try started working on phase one in 2022. Costs have soared due to Covid delays and wider industry cost inflation.
To find extra cash, the council cabinet this week approved reducing the Woodlands development budget east of Aylesbury and the Eastern Link Road South.
Martin Tett, Leader of Buckinghamshire Council, said: “Buckinghamshire urgently needs the right infrastructure in place, so it’s great news that we’ve been able to approve the delivery of the South East Aylesbury Link Road.
“Despite price inflation for all major infrastructure projects, we now have firm contractor costs for the SEALR project.
“Our Cabinet decision bridges the funding gap for this complex project without any cost to the taxpayer, thanks to the allocation of external funding.
“We continue to remain committed to working with third parties to deliver the Eastern Link Road (South), the Southern Link Road, and the South West Aylesbury Link Road.”