The mile-long Northern Inner Distributor Road (NIDR) now links the east of the town with the west.
It was estimated in January that technical issues involving a bridge increased the cost of the £21m project by a further £10m.
The council is in a legal dispute with the contractor Carillion about the extra costs and who should pay.
Somerset County Council said the delays had been "enormously frustrating".
Cabinet member for highways, John Woodman, said the new road will "unlock" the old cattle market Firepool site for development and ease traffic in the town.
He added: "The dispute is ongoing and we will work hard to make the best result for all the people of Somerset and the people of Taunton."
Mike Rigby, independent councillor for Bishops Lydeard, said the council had "a lot of questions" to answer about how the project was managed.
"How has it been that the council signed a contract that enabled a contractor to take more than twice the amount of time to build what should be a fairly straight-forward job?
"It worries me, it's [an] example of how the county council has not well-managed a large contract."
Carillion had nothing to add to the council statement.
A multi-million pound road scheme to ease congestion in Taunton has opened more than two years behind schedule.