Tax officials will have to disclose to MPs how Starbucks managed to use legal loopholes to pay less than 1% tax in its 14 years of UK trading, as part of the investigations.
The probes will also take a broad look at big corporations and how they pay their tax, likely to include Facebook.
It is thought that one area that MPs will look at will be the practice of diverting UK profits through offices outside of UK to parts of Europe with lower corporation tax rates.
There are to be two probes - one from the Public Accounts Committee (PAC) and one from the Treasury. There is no evidence that Starbucks and Facebook have done any wrongdoing. But the two probes will be wide-ranging in looking at the tax affairs of big UK corporations.
Margaret Hodge, chair of PAC, said: "HMRC must take a serious look into these allegations against Starbucks. It is certainly something my Committee will expect official to address when we re-visit the issue of tax avoidance before Christmas.
"Ordinary people and small businesses, who pay their taxes in full and without question, will rightly be furious that yet again a highly profitable global corporation has wriggled out of paying its fair share. It is just not right.
"My own view is that the government must find a way of lifting the veil of secrecy that prevents us from knowing about what these companies area up to, simplify the tax system so that there are fewer loopholes to exploit and ensure that there are enough people with the right skills inside HMRC to take on these big companies and their armies of lawyers.
"Everyone should be equal before the law, and tackling tax avoidance is also crucial to getting down the deficit. We simply cannot continue with a system that allows a company like Starbucks to get away with paying no tax whatsoever."
Investigations of this nature could lead to recommendation on how to change tax law to prevent companies from shifting profits overseas.
A spokesperson for Facebook said: "As is normal for an organisation operating in dozens of countries around the world, we regularly file reports about local operations. The information does not necessarily present a full account of overall global financial performance so it would be a mistake to draw any conclusions from these filings."
Starbucks has mounted a defence on its website. Kris Engskov, UK managing director, said: "The most important thing to understand is that Starbucks does pay tax in the UK. Indeed over the last three years we have paid over £160m in various taxes including National Insurance contribution for our 8,500 UK employees, and business rates. "
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