BRUSSELS—Ireland will begin collecting €13 billion ($15.46 billion) in back taxes from Apple Inc. as soon as early next year after both sides agreed to the terms of an escrow fund for the money, Ireland’s finance chief said Monday.

The European Union in 2016 ordered Dublin to retrieve the billions of euros from Apple in uncollected taxes, which the EU said Apple avoided paying with the help of sweetheart tax deals from Ireland.

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