The Attorney-General has agreed to a new inquest into the Stardust tragedy.
Some 48 people died in the nightclub fire in the Artane area of Dublin on Valentine's night in 1981.
The families have continuously called for answers into the cause of the blaze.
Attorney-General Seamus Woulfe wrote to the representatives of the relatives today.
In a statement, the Office of the Attorney-General said: "Having carefully considered all aspects of the matter the Attorney-General has formed the opinion that fresh Inquests into the Stardust deaths are advisable.
"This is because he considers that in the original inquests there was an insufficiency of inquiry as to how the deaths occurred, namely, a failure to sufficiently consider those of the surrounding circumstances that concern the cause or causes of the fire.
"The Attorney-General is thus satisfied that the holding of fresh inquests is, on balance, in the public interest and in the interests of justice."
The campaign group Justice for Stardust said: "This is amazing news, we never believed this day would come as you can imagine we are completely overwhelmed with the news and would ask that people give us space tonight to be with our families to absorb it."
Darragh Mackin, of law firm Phoenix Law which acts for the Stardust Truth and Justice Committee, said the families "are delighted" with today's decision.
They're due to hold a press conference at Dublin's Buswells Hotel tomorrow morning.