Apple has been ordered to repay €13 billion in tax by the EU
The penalty is largest EU fine to date, smashing the €1.4 billion (£1.2 billion; $1.6 billion) levied against French energy giant EDF in 2015.
Margrethe Vestager, the EU's competition commissioner, is due to announce the fine on Tuesday.
"Member States cannot give tax benefits to selected companies - this is illegal under EU state aid rules," said Vestager in a press release ahead of her speech. "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 per cent in 2014."
The European Commission started to look into Apple's Irish tax rate in 2014, so the decision is the culmination of a three-year investigation.
The Commission concluded that Apple received "illegal state aid" from Ireland - essentially a sweetheart deal that allowed the computer maker to unfairly reduce its tax bill in a way not available to other companies.
However, the Irish government and Apple are likely to appeal the ruling, which could push back the final decision by five or six years, according to The Irish Independent.
The size of the penalty was first tweeted by Tony Connelly, the European editor of Irish broadcaster RTE.
A follow-up tweet from Connelly said: "Commission to say "selective treatment" allowed Apple to pay tax rate of 1pc on EU profits in 2003 down to 0.005 per cent in 2014."
The fine is likely to trigger one of the world's biggest tax disputes and a political showdown between Europe and the US.
The Obama administration has been watching the case with concern, and warned the Commission of potential consequences if it ruled against Apple and Ireland.
The US Treasury said in a white paper published last Wednesday that it "continues to consider potential responses should the Commission continue its present course," and accused the Brussels investigation of being "supranational."
Apple CEO Tim Cook has criticised the international tax system as "not good," and has vowed to appeal the decision if he feels that Apple didn't "get a fair hearing."
"Let me explain what goes on with our international taxes. The money that's in Ireland that he's probably referring to is money that is subject to US taxes. The tax law right now says we can keep that in Ireland or we can bring it back," Cook told The Washington Post.
"It's important for everyone to understand that the allegation made in the EU is that Ireland gave us a special deal. Ireland denies that," Cook said. "The basic controversy at the root of this is, people really aren't arguing that Apple should pay more taxes. They're arguing about who they should be paid to. And so there's a tug of war going on between the countries of how you allocate profits."