The Lincoln Eastern Bypass will cost £120 million instead of £99 million and will also be finished in May 2020 instead of December 2019.
The news comes as Lincolnshire County Council appointed Galliford Try as the replacement firm to finish work on the project following the collapse of Carillion in January.
The new 7.5km single carriageway road is set to minimise congestion in the city, but the project will be late and over budget.
In addition to the Heighington Road bridge and Greetwell Road roundabout, Galliford Try will also be overseeing construction of the Hawthorn Road footbridge, South Delph footbridge and the River Witham Bridge, including its fabrication, supply and assembly.
Cllr Richard Davies, executive member for highways, said: “Since taking over from Carillion, Galliford has made great progress on-site, so we’re excited to continue building this relationship as they oversee all of the milestones to come, including the construction of four new roundabouts, two major bridges and 7.5km of new road.
“There are always unknowns when taking on a project of this scale, but we now have a much clearer picture of where the project stands.
“At this stage, the total cost of the project is now expected to be £120 million, with about half the new costs coming as a result of changing contractor and the remainder from additional archaeological spend, additional land acquisition costs and inflation.
“Also, another outcome of Carillion’s collapse is that the scheme’s new expected completion date is May 2020.
“We know this isn’t ideal, as were hoping for the bypass to be open in December 2019, but we have done all we can to keep the project moving in the right direction.
“By exploring all options and focusing our efforts on getting the best value for money, we’ve been able to keep the time delay to a minimum, despite the situation we were cast into.
“The Lincoln Eastern Bypass is the city’s biggest road project in decades, and we’re glad to have now reached a resolution to this situation so we can concentrate fully on delivering a scheme that will offer a wide range of benefits to those traveling in and around Lincoln.”