According to a US spending bill passed last Friday, each of the 53 hostages or their estates would receive up to $4.4 million.
The victims of other state-sponsored terror attacks such as the US embassy bombings in East Africa in 1998 would also be eligible.
The hostage-taking lasted 444 days and led the US to break off ties with Iran.
The decision to award compensation followed a controversial deal between world powers and Iran over its nuclear programme.
The hostages have long fought for restitution, but the agreement that secured their release, barred them from making such claims and their attempts were repeatedly blocked by the courts, including an appeal denied by the Supreme Court.
The Congress was also unable to pass laws granting them compensation.
The money for compensation is likely to come from a huge $9 billion fine for French bank Paribas for violating sanctions against Iran, Sudan and Cuba, the New York Times reported.
About $1 billion will go into a fund for victims of terrorism and an additional $2.8 billion will be set aside to help the victims of the 9/11 attacks and their families.
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