The Guildhall redevelopment is set to go £1.5 million over budget.
The project to repair and revamp the historic building is now set to cost £21.7 million.
Work has progressed on the scheme throughout the pandemic – but it has been hit by delays including the archaeological discovery of human remains and a need to redesign the underpinning of the structure.
The contractor has been given an extra 21 weeks to work on the project – and the costs associated with this as well as the additional work required has caused the cost to rise, according to a City of York Council report.
It says other cash within the council’s major projects budget has been found to help fund the project.
The report adds: “Work continues on site through a further winter period and the risks of further delay because of high river levels and the potential impact of Covid 19 on site operations remain.
“Officers will continue to work closely with contractors to ensure the project is delivered by summer 2021.”
A £300,000 grant has been given to the council to fit out the offices.
And it has been announced that the building will be leased to York Science Park (YSPL), a subsidiary of the University of York.