The contractor – which is part of the Highlands based Anderson Construction Group – has blamed delays on bad weather and skills shortages in Shetland.
The council is now looking for a new contractor to complete the job.
Robert Sinclair, Executive Manager of Capital Programme Service, said: “We’ve had some useful talks with the contractor over recent weeks and have agreed with them that this is the best way forward.
“The Council is now looking forward to getting the job finished. We’re confident of getting another contractor on board in the near future.”
Martin Anderson, Managing Director of Airport Civil Engineering said: “I’m glad that we’ve been able to resolve matters so quickly and to be able to do so by mutual agreement.”