EU officials are looking at whether the countries' tax treatment of multinationals, which help to attract investment and jobs that might otherwise go to where the companies' customers are based, represent unfair state aid.
Corporate tax avoidance has risen to the top of the international political agenda in recent years following reports of how companies such as Apple and Google use convoluted structures to slash their tax bills.
Governments have promised to rewrite the rules that govern international tax, but experts said the European Commission would struggle to make any challenge to the deals Ireland, Luxembourg and the Netherlands had agreed under existing rules.
Apple said it had not received any selective tax treatment from the Irish authorities, while the Irish government said it was confident it had not breached state aid rules and would defend its position vigorously.
Fiat declined to comment and Starbucks was not immediately available.
Sheila Killian, assistant dean in the accounting & finance department of Limerick University, Ireland, said the announcement, naming individual companies, represented a more aggressive stance from the Commission.
She said: "It's upping the ante from the EU's point of view."
The Commission said it was looking at whether the pricing for transactions between company subsidiaries - known as transfer pricing - that were approved by the Irish, Luxembourg and Dutch tax authorities and which allowed the companies to reduce their tax bills, were selective and thereby represented unfair incentives.
But Ms Killian said international tax rules gave companies wide flexibility in choosing transfer prices and so the legal hurdles the Commission faced were substantial.
She added: "It is almost impossible to prove the transfer pricing is any way favourable but in launching a high-profile investigation, it puts a spotlight on those companies' tax affairs, which acts as a deterrent to companies against engaging in aggressive tax planning."
A Commission spokesman denied the aim of the investigation was to act as a deterrent. He was unable to name a single case where the Commission had successfully challenged a country's transfer pricing decisions.
Starbucks told a UK Parliamentary investigation in 2012 it received a tax deal in the Netherlands that allowed it to enjoy a "very low" tax rate, while a US Senate probe last year revealed Apple had sheltered tens of billions of dollars in profits from tax by using Irish companies that had no tax residence anywhere.
In the US, Apple entered into deals with the Irish subsidiaries whereby the Irish units received the rights to certain intellectual property that were subsequently licensed to other group companies, helping ensure almost no tax was reported in countries such as Britain or France.
Apple's Irish arrangement helped it achieve an effective tax rate of just 3.7 per cent on its non-American income last year.