The European Commission had ordered Dublin to collect the money in 2016 after concluding that two Irish tax rulings allowed Apple to pay less tax than other businesses.
The European Commission (which made the original ruling) expects the money to be transferred to an escrow account during the first quarter of the new year.
Ireland expects the United States iPhone maker to start paying billions in back taxes, after the European Union said in 2016 the money was the result of Apple receiving unfair tax incentives and launching a lawsuit against Ireland. The unfair advantage resulted in Apple avoiding as much as 13 billion euros in payments over the course of more than a decade.
Finance Minister Paschal Donohoe told reporters before a meeting with European Competition Commissioner Margrethe Vestager on Monday that Ireland and Apple had reached an agreement to "the principles and operation of the escrow fund" into which the U.S. iPhone maker was expected to pay the money.
The government have come to an agreement with Apple for the contested €13 billion tax bill that the company was ordered to pay Ireland.
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iPhone maker Apple has agreed to pay Ireland $15.46 billion in back taxes by early 2018.
Amazon denied it owed any back tax, saying it did "not receive any special treatment from Luxembourg".
However, Apple added that it remains confident that the court will overturn the commission's decision after reviewing and reading the evidence they have presented in their defense.
According to the EU, the tax deal allowed Apple to pay nearly nothing in tax on its European profits between 2003 and 2014.