The Lord Chief Justice Lord Judge and two other judges made the ruling at the High Court in London after an application by the Attorney General Dominic Grieve.
"Great news! Accidental verdict been squashed," Aldridge, who was in the team which played in the abandoned semi-final 23 years ago, wrote on Twitter.
"IT HAD TO HAPPEN. A new investigation on the police as well. And that HAD TO HAPPEN too. YNWA."
Kenny Dalglish, manager at the time, was a key figure in dealing with the aftermath of the disaster and a major supporter of the families' search for justice.
"Two fantastic results today for the Hillsborough families. Your support has been unbelievable," he wrote on Twitter.
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