The decision is based on the Commission’s criticism of abuse of state aid rules, which it claims Ireland has used to attract investment and minimise tax bill for Apple. It is a retrospective decision dating back to tax arrangements made since 2003.

As the announcement was made Apple’s shares fell 1.6%.

Ireland immediately announced plans to appeal the Commission’s decision. Under EU rules, it must still recover the illegal state aid but could, for example, place the recovered amount in an escrow account pending the outcome of the EU court procedures.

In an early reaction to the news, Michael Noonan, minister for finance, indicated he had ‘no choice’ but to launch an appeal.

‘This is necessary to defend the integrity of our tax system; to provide tax certainty to business; and to challenge the encroachment of EU state aid rules into the sovereign member state competence of taxation,’ he said.

In a statement, Apple said: 'The European Commission has launched an effort to rewrite Apple's history in Europe, ignore Ireland's tax laws and upend the international tax system in the process.

'The commission's case is not about how much Apple pays in taxes, it's about which government collects the money. It will have a profound and harmful effect on investment and job creation in Europe.

'Apple follows the law and pays all of the taxes we owe wherever we operate. We will appeal and we are confident the decision will be overturned.'

Margrethe Vestager, the commissioner in charge of competition policy, said: ‘The Commission's investigation concluded that Ireland granted illegal tax benefits to Apple, which enabled it to pay substantially less tax than other businesses over many years. In fact, this selective treatment allowed Apple to pay an effective corporate tax rate of 1% on its European profits in 2003 down to 0.005% in 2014.’

The Commission has demanded that Apple repay the retrospective tax bill together with interest earned although this will be fiercely fought at the Commission.

The investigation, launched in June 2014, found that two tax rulings issued by Ireland to Apple ‘substantially and artificially’ lowered the tax paid by Apple in Ireland since 1991.

The rulings endorsed a way to establish the taxable profits for two Irish incorporated companies of the Apple group (Apple Sales International and Apple Operations Europe), which did not correspond to economic reality: almost all sales profits recorded by the two companies were internally attributed to a so-called ‘head office’, it found.

The Commission's assessment showed that these ‘head offices’ existed only on paper and could not have generated such profits. These profits allocated to the head offices were not subject to tax in any country under specific provisions of the Irish tax law, which are no longer in force.

The Commission said the head office did not have any employees or own premises, while only the Irish branch of Apple Operations Europe had the capacity to generate any income from trading, Therefore, sales profits of Apple Operation Europe should have been recorded with the Irish branch and taxed there.

As result, the Commission says Ireland must now recover the unpaid taxes from Apple for the years 2003 to 2014 of up to €13bn, plus interest.

It claims the tax treatment in Ireland enabled Apple to avoid taxation on almost all profits generated by sales of Apple products in the entire EU single market, as Apple decided to record all sales in Ireland rather than in the countries where the products were sold. If other countries were to require Apple to pay more tax on profits of the two companies over the same period under their national taxation rules, this would reduce the amount to be recovered by Ireland.

Apple Sales International and Apple Operations Europe are two Irish incorporated companies that are fully-owned by the Apple group, ultimately controlled by the US parent, Apple Inc. They hold the rights to use Apple's intellectual property to sell and manufacture Apple products outside North and South America under a so-called 'cost-sharing agreement' with Apple Inc.

Under this agreement, Apple Sales International and Apple Operations Europe make yearly payments to Apple in the US to fund research and development efforts conducted on behalf of the Irish companies in the US. These payments amounted to about $2bn (£1.53bn) in 2011 and significantly increased in 2014.

These expenses, mainly borne by Apple Sales International, are deducted from the profits recorded by Apple Sales International and Apple Operations Europe in Ireland each year, in line with applicable rules originally determined by a tax ruling granted by Ireland in 1991, which in 2007 was replaced by a similar second tax ruling. This tax ruling was terminated when Apple Sales International and Apple Operations Europe changed their structures in 2015.

Apple set up their sales operations in Europe in such a way that customers were contractually buying products from Apple Sales International in Ireland rather than from the shops that physically sold the products to customers. In this way Apple recorded all sales, and the profits stemming from these sales, directly in Ireland.

Therefore, the Commission said, only a small percentage of Apple Sales International's profits were taxed in Ireland, and the rest was taxed nowhere. It calculated that in 2011, Apple Sales International recorded profits of $22bn (€16bn) but under the terms of the tax ruling only around €50m was considered taxable in Ireland, leaving €15.95bn of profits untaxed.

As a result, Apple Sales International paid less than €10m of corporate tax in Ireland in 2011 – an effective tax rate of about 0.05% on its overall annual profits. In subsequent years, Apple Sales International's recorded profits continued to increase but the profits considered taxable in Ireland under the terms of the tax ruling did not. Thus this effective tax rate decreased further to only 0.005% in 2014.

On this basis, the Commission concluded that the tax rulings issued by Ireland endorsed an artificial allocation. However it pointed out that its decision does not call into question Ireland's general tax system or its corporate tax rate.

Its methodology for calculating the value of the undue competitive advantage enjoyed by Apple requires Ireland to allocate to each branch all profits from sales previously indirectly allocated to the head office of Apple Sales International and Apple Operations Europe, respectively, and apply the normal corporation tax in Ireland on these re-allocated profits. The decision does not ask for the reallocation of any interest income of the two companies that can be associated with the activities of the head office.

Around €50m in unpaid taxes relate to the undue allocation of profits to the head office of Apple Operations Europe, and the remainder to allocations to the head office of Apple Sales International. The recovery period stops in 2014, as Apple changed its structure in Ireland as of 2015 and the ruling of 2007 no longer applies.

The amount due would decrease if other EU countries decided to take action, and would also be reduced if the US authorities were to require Apple to pay larger amounts of money to their US parent company for this period to finance research and development efforts. 

The Commission is also investigating state aid arrangements over agreements between Luxembourg tax authorities and multinationals Amazon and McDonald's.