Alun Griffiths told the council in March that it would not be building the bypass it had started enabling works on the month before.
Main construction work was due to start this spring but was put on hold while the hunt started for a replacement contractor.
Galliford Try’s first task will now be the completion of preparatory works and any remaining detailed designs to discharge remaining planning conditions.
Councillor Mike Bell, Leader of North Somerset Council and Executive Member for Major Projects, said: “Banwell bypass is a scheme we’re immensely proud of and keen to deliver and, despite setbacks over these past few months, I’m pleased to say that we’re still on track toward starting construction this year.
“Working with Galliford Try has been incredibly positive so far and I’m excited to continue our work together as we get the scheme delivered.”
Liz Bell, Operations Director at Galliford Try, said: “We are delighted to be working together with the North Somerset team to bring this project forward, and help play our part in improving the lives of local people.”
The contract with Galliford Try is in two stages. The first stage includes preparatory works and detailed design and the second includes main construction. North Somerset Council will take a decision on proceeding with the second stage of the contract at Full Council in the autumn.
Banwell bypass is funded through Homes England’s Housing Infrastructure Fund.