40 units will see up to 320 people accommodated.
Modular units at a former Westmeath army barracks are expected to be completed by the end of the year.
Tented accommodation at Columb Barracks in Mullingar is set to be replaced by 40 units, and will represent the first project in the Department of Integration's new scheme.
The new accommodation will have the capacity to house up to 320 International Protection Applicants.
It comes after it was revealed the cost of modular housing has more than doubled, with each unit costing around €442,000.
Integration Minister, Roderic O'Gorman says he expects the handover of the Mullingar site to begin this month:
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