The move follows talks at arbitration service Acas which aimed to settle a dispute arising from the local authority's proposed £150m IT outsourcing contract, which would see the workers' jobs transferred to either Capgemini or ITNet. The IT workers are calling for secondment rather than transfer.
The return to work came as a ballot of 5,000 Unison members returned a 63% vote to strike against outsourcing.
A Swansea Council spokesman said, "We welcome the decision by IT staff to return to work. We always believed that this dispute would be resolved through negotiation with Acas.
"However, on the wider issue of privatisation and redundancies, we are disappointed that Unison has decided to take strike action. We do not believe there is a need for strike action."