Provincial officials say IBM extended 72 offers, which were accepted by 28 people.
Fourteen of those who accepted were unionized department employees.
Union officials say the rest worked for the province's Capital Health authority.
The employees manage the SAP computer system, which includes payroll, procurement, human resources and other information.
Premier Darrell Dexter announced the untendered deal to contract the work to IBM in November, saying the company plans to hire 500 employees in eight years.