DUBLIN—Ireland passed a final review from its international creditors on Thursday, setting it up to become the first bailed-out euro-zone country to return fully to the bond markets for its financing needs.

The positive review by the European Central Bank, the European Commission and the International Monetary Fund reflects Ireland's success in cutting its budget deficit, as well as the progress made in repairing a banking system that was wrecked six years ago by the calamitous collapse of the country's property market.

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