Apple's €13bn Irish tax bill will be paid this year, the finance minister said.
Paschal Donohoe said he expected the recovery of funds to be completed in the coming months after signing a detailed legal agreement on the refund of what the EU alleges is state aid from the technology giant.
The European Commission said in 2016 that the multinational had received unfair tax incentives from Ireland and ordered it to pay back taxes to the state.
Mr Donohoe said: "This is a significant milestone with regard to the commencement of the recovery of the alleged state aid, as the Escrow Framework Deed is the overarching agreement which will govern the collection and eventual payment of funds."
The Commission found that Ireland had given Apple illegal state aid by allowing it to pay an effective 1% corporation tax.
Apple and the Government are appealing the Commission's ruling on the grounds that the tax treatment did not break Irish or EU law.
The money will be held in an escrow account meaning the proceeds cannot be released until there has been a final determination in the European courts over the validity of the Commission's decision.
The Bank of New York Mellon, London branch, Amundi, BlackRock Investment Management (UK) Limited and Goldman Sachs Asset Management International have been selected as preferred tenderers for the provision of services related to the money.
The Finance Department said: "It is anticipated that the funds will flow into the escrow fund in significant tranches.
"It is expected that the full recovery will be effected by the end of quarter three, 2018."
Ireland's open economy is based on using low corporate taxation among other incentives to attract multinationals. In Apple's case it was significantly below the standard 12.5% imposed on income.
The Government opposes any effort to force it to change its taxation practices, which have seen the world's top financial and technology firms set up base in Dublin.
Minister Donohoe reiterated his Government's fundamental disagreement with the Commission's Apple decision.
He added: "However, as committed members of the European Union, Ireland is intent on complying with our binding legal obligations in this regard.
"This is the largest recovery fund of its kind ever to be established and due to the complexity of such, together with our duty to comply with EU procurement rules, it has taken some time to get to this point.
"I am happy that I can sign the deed with Apple today, which has been the subject of difficult and intensive work.
"Once the infrastructure associated with the escrow is put in place, following the execution of the deed, I expect that recovery of the funds will be completed by end quarter three, 2018."