BRUSSELS—Europe’s competition chief has ordered Ireland to reclaim €13 billion (£11.1 billion/$14.5 billion) in back taxes from Apple.

It comes despite the US treasury department warning last week that it would “consider its options” in such an eventuality.

Speaking at the European Commission’s headquarters in Brussels on Tuesday, Margrethe Vestager said: “Member states cannot give tax benefits to selected companies—this is illegal under EU state aid rules."

The investigation, which started in 2014, has technically not found Apple guilty of wrongdoing. Rather it is a judgment that the so-called sweetheart tax deals Apple received from Ireland constitute illegal state aid.

Because the commission can order recovery of illegal state aid for up to 10 years before first request for information, Ireland must now recover the unpaid taxes from Apple for the years 2003 to 2014, plus interest.

“This is not a penalty, it is unpaid taxes to be paid,” said Vestager who was scathing about Apple’s activities. “The so-called ‘head office’ did no business. It had no employees, no premises. But under the tax ruling the so-called head office was attributed all the company’s profits for sales throughout Europe Africa, Middle East, and India,” she added.

“Tax rulings cannot endorse a method that fails to reflect economic activity or reality, for that matter,” the commissioner said.

Brussels' officials said that Ireland allowed Apple to pay an effective corporate tax rate of one percent on its European profits in 2003 down to 0.005 per cent in 2014. These were determined by tax rulings granted in 1991 and 2007. This tax ruling was terminated in 2015.

“It is for the Irish authorities to determine the exact amount—working out the interest due—and the modalities of reclamation,” said Vestager. However she stood by the massive €13 billion figure: “There is no discretion for me to choose, it is based on the facts and I hope that if it goes to court it will be upheld as it is based on facts.”

Apple established two companies—Apple Operations Ireland and Apple Sales International—but almost all sales profits recorded by these two entities were attributed to a "head office" that Vestager said “existed only on paper and could not have generated such profits,” adding that the “situation did not correspond to economic reality.”

Apple Sales International and Apple Operations Europe did make payments to Apple in the US to fund research and development of around $2 billion a year.

The amount Apple must pay could be reduced if the US Internal Revenue Service (IRS) determines that the Irish subsidiaries should dish out a larger amount to Apple US to pay for research and development. How much it might be reduced by is unclear, however.

“The details on this can be quite difficult to assess, because this is up to the US authorities,” Vestager said.

The commission estimates that around €187 billion of profits are not repatriated to the US. “Therefore, only a small percentage of Apple profits were taxed in Ireland, and the rest was taxed nowhere,” it said.

Apple's boss Tim Cook, in a lengthy statement rebuffing the ruling, accused the European Commission of trying "to rewrite Apple’s history in Europe, ignore Ireland’s tax laws, and upend the international tax system in the process." He added:

The opinion issued on August 30 alleges that Ireland gave Apple a special deal on our taxes. This claim has no basis in fact or in law. We never asked for, nor did we receive, any special deals. We now find ourselves in the unusual position of being ordered to retroactively pay additional taxes to a government that says we don't owe them any more than we've already paid. The commission’s move is unprecedented and it has serious, wide-reaching implications. It is effectively proposing to replace Irish tax laws with a view of what the commission thinks the law should have been. This would strike a devastating blow to the sovereignty of EU member states over their own tax matters, and to the principle of certainty of law in Europe.

Cook added that Apple would appeal against the ruling, adding: "We are confident that the commission’s order will be reversed."

He claimed that the iPhone maker had been singled out by Brussels' officials. Cook said:

In Apple’s case, nearly all of our research and development takes place in California, so the vast majority of our profits are taxed in the United States. European companies doing business in the US are taxed according to the same principle. But the commission is now calling to retroactively change those rules. Beyond the obvious targeting of Apple, the most profound and harmful effect of this ruling will be on investment and job creation in Europe.

Ireland has also said it will appeal against the decision in Europe's courts. The country's finance minister, Michael Noonan, said he “profoundly” disagreed with the commission’s findings. He said it was “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 added: “It is important that we send a strong message that Ireland remains an attractive and stable location of choice for long-term substantive investment.”

Vestager said there were "many ways for countries to encourage companies to invest in Europe. It is up to Ireland whether they want to challenge [the ruling] or not." However, she also invited other jurisdictions to look at the commission’s findings to see if they believe Apple owes profits elsewhere. Such a situation could provoke a free-for-all where other member states vie for a slice of the apple.

“This is not about transfer pricing, it is about allocation of profits so it is different to the decisions on Starbucks and Fiat,” Vestager told reporters.

The US treasury department will also look closely at the decision to evaluate if Apple’s US tax liability is reduced. “This would effectively constitute a transfer of revenue to the EU from the US government and its taxpayers,” warned a treasury white paper last week.

Meanwhile, the commission continues to investigate a similar case relating to Amazon's tax structure.

This story was updated after publication with comment from Apple CEO Tim Cook.