Each of the 53 hostages or their estates will receive up to $4.4m (£3m), according to a US spending bill passed last Friday.
The victims of other state-sponsored terror attacks such as the US embassy bombings in East Africa in 1998 will also be eligible.
The hostage-taking lasted 444 days and led the US to break off ties with Iran.
The decision to award compensation follows a controversial deal between world powers and Iran over its nuclear programme.
"Those negotiations resulted in an understanding that an inevitable next step in securing a relationship was to address the reason for the rupture, which was our kidnapping and torture," former hostage Rodney Sickmann told the New York Times.