The company’s special arrangement with Luxembourg dates back to 2003 when European Commission president Jean-Claude Juncker was prime minister.
But the deal was under investigation for three years and a preliminary ruling by the European Commission said the deal “constituted state aid”.
European Competition Commissioner Margrethe Vestager said: “Luxembourg gave illegal tax benefits to Amazon.
“As a result, almost three quarters of Amazon’s profits were not taxed.”
Ms Vestager said the exact amount of tax to be reclaimed would still need to be calculated.
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The Commission found Luxembourg allowed Amazon to channel a significant portion of its profits to a holding company without paying tax.
The holding company was allowed to do this because it held certain intellectual property rights.
Officials said: “The Commission’s investigation showed that the level of the royalty payments, endorsed by the tax ruling, was inflated and did not reflect economic reality.”
Amazon, which employs 1,500 in Luxemburg, is one of the biggest employers in the country of half a million people.
A company spokesman said: “We believe that Amazon did not receive any special treatment from Luxembourg and that we paid tax in full accordance with both Luxembourg and international tax law.”
Amazon revamped its European tax practices in 2015 so that it can book sales and pay taxes in Britain, Germany, Spain and Italy instead of channeling all sales through Luxembourg where it has its headquarters.
Luxembourg, whose tiny economy has benefited from providing a welcoming European home for multinational companies, rejected the finding and said it was looking at its legal options.
Mr Juncker was prime minister of there for almost two decades until 2013 and has been criticised for his role in enabling the many tax deals which are now being unravelled.
He denies doing anything wrong and says the Commission is committed to ensuring fair taxation.
The country made international headlines in 2014 over the publication of documents which showed how large accounting firms helped multinational companies channel proceeds through the country while paying little to no tax.
Luxembourg is also under EU scrutiny over tax deals with fast food chain McDonald’s and French energy company Engie.
The country has appealed against a ruling in 2015 that carmaker Fiat should pay it back taxes.
Multinational companies have come under fire since the global financial crisis for shifting profits between subsidiaries to use the gaps between countries to minimise taxes.
The Amazon ruling has has echoes of the European Commission case against Apple which resulted in an £11.5bn bill being slapped on the US technology giant for Irish back taxes.
Brussels claimed Dublin had given Apple, which employs about 4,000 people in the Republic, illegal state aid through special tax arrangements. Apple is appealing against the ruling.