They were convicted of stealing money with some imprisoned, because of the Post Office's defective Horizon accounting system.
The post office workers have finally had their names cleared by the Court of Appeal on Friday, April 23.
Announcing the court's ruling, Lord Justice Holroyde said the Post Office "knew there were serious issues about the reliability of Horizon" and had a "clear duty to investigate" the system's defects.
But the Post Office "consistently asserted that Horizon was robust and reliable" and "effectively steamrolled over any subpostmaster who sought to challenge its accuracy", the judge added.
Lord Justice Holroyde said: "Post Office Limited's failures of investigation and disclosure were so egregious as to make the prosecution of any of the 'Horizon cases' an affront to the conscience of the court."
However, three of the former subpostmasters - Wendy Cousins, Stanley Fell and Neelam Hussain - had their appeals dismissed by the court.
Lord Justice Holroyde said the Court of Appeal had concluded that, in those three cases, "the reliability of Horizon data was not essential to the prosecution case and that the convictions are safe".
Nick Read, Post Office chief executive said: "I am in no doubt about the human cost of the Post Office's past failures and the deep pain that has been caused to people affected.
"Many of those postmasters involved have been fighting for justice for a considerable length of time and sadly there are some who are not here to see the outcome today and whose families have taken forward appeals in their memory. I am very moved by their courage.”
There were 73 convictions in Scotland caused by the failure.
Although a total of 47 postmasters in England and Wales have had their cases referred to the Appeal Court, there has never been similar action in Scotland.
However, now the Scottish Criminal Cases Review Commission (SCCRC) has written to the people it believes may also have been the victims of possible miscarriages of justice in Scotland relating to the Horizon computer system.
One former sub-postmaster Phil Cowan and his partner Fiona McGowan were falsely accused of stealing thousands of pounds.
The couple were visited by their area manager after weeks of discrepancies at their branch in Parsons Green, Edinburgh, culminating in a £30,000 shortfall.
She spiralled into depression after being wrongly accused and passed away in her sleep in 2009, aged 47, after accidentally overdosing on anti-depressants and alcohol, leaving two sons, age 12 and 14.
The SCCRC letter says: "We are currently investigating possible miscarriages of justice relating to problems with the Post Office’s Horizon computer system. We think that it is possible that your case is one of those. If it is, we would like to make sure that you have the chance to apply to us.
"The Post Office identified your case as a Scottish prosecution during the relevant period (from 1999) in which they may have been involved. We asked Crown Office (the procurator fiscal service) to use the Post Office information to find your contact details. They helped us with that."