Parliament passed the law three weeks ago – although there were some sceptical voices in the coalition government of Social Democrats (SPÖ) and conservative People's Party (ÖVP).
Fischer's office announced on Thursday that the President had evaluated the law with his councillor on legal issues, former President of the Constitutional Court Ludwig Adamovich.
After that Fischer decided to sign the law and to "open the way for a further examination of constitutional issues by the Constitutional Court."
Ratings agencies have said that the law was setting a dangerous precedent. It should ensure that investors in Hypo – not just taxpayers – help to shoulder the financial burden of winding down a bank that has sucked in €5.5 billion in public aid so far.
Moreover it could drive up borrowing costs for other state-backed firms, including utilities and health agencies.
Some creditors like the World Bank or Austrian insurance companies have already announced that they will sue for damages.
Finance Minister Michael Spindelegger (ÖVP) has argued that this law will save the taxpayer €1.7 billion, and prevent the bankruptcy of the Carinthian province.