Parts of the mixed-use scheme were left unfinished when main contractor Buckingham Group went into administration last September after completing most of the job.
Willmott Dixon was drafted-in shortly after to finish the car park and some snagging work at the site with about £5m worth of work left to do.
But between then and now Willmott Dixon and Swansea Council have had a change of heart about its role on the project.
The council has now appointed Andrew Scott to complete work following “Willmott Dixon undertaking detailed site surveys to establish the scope of the finishing works needed.”
Cllr Rob Stewart, Swansea Council Leader, said: “The council acted quickly following Buckingham Group going into administration to protect our position and appoint Willmott Dixon to establish the scale and scope of the works needed on site to complete the Copr Bay development.
“We’d like to thank Willmott Dixon for their guidance and survey work, which will now inform the work that Andrew Scott Ltd will be carrying out.
“The completion of the car park, retail units and other finishing works will follow-on from a project that’s already delivered Swansea Arena, the coastal park, the car park under the arena and the new bridge over Oystermouth Road.
“These facilities have already benefitted hundreds of thousands of local people and visitors to the city.”