The Post Office has said it will not oppose dozens of appeals from sub-postmasters accused of stealing from the company.
It means the convictions - which have been against the names of many for almost 20 years - will now be quashed by the Court of Appeal.
From the early 2000s, over a period of 15 years, hundreds were accused of theft and fraud. However, during those years, a faulty computer system was causing money to disappear from accounts.
A total of 47 sub-postmasters had been referred to the Court of Appeal by the Criminal Cases Review Commission. Just three of the appeals were contested by The Post Office on Friday.
The Horizon computer system was first installed into Post Offices back in 1999. However, by the early 2000s, money had started disappearing from accounts.
Over the next 15 years, around 900 postmasters and mistresses were charged with fraud and theft, with some jailed.
Recently, some 550 of them fought back, banding together and taking the Post Office to court.
In December last year, The Post Office paid out in a £58 million pound settlement. This prompted the criminal appeals process.
Solicitor Neil Hudgell, who represented over two-thirds of the sub-postmasters, says Friday marked a "landmark moment".
He said: "It is of course now a matter for the Post Office as to whether it would seek any retrials, but we have been given no indication of that happening. It's something which would need significant consideration as to the public interest in doing so, given the huge public support for those affected.
“We are today obviously delighted for the people we represent. Clearing their names has been their driving goal from day one, as their reputations and livelihoods were so unfairly destroyed."
Mr Hudgell added that those with quashed convictions endured "years of suffering" and said the convictions had not only impacted the individuals, but their loved ones too.
“People were forced into admitting to crimes they had not committed simply because they were told this computer system was infallible," Mr Hudgell continued."They were basically told they’d likely face prison if they continued to plead innocence as they’d be found guilty in court. They were told that they’d be better placed to effectively make up a story as to where the money went."
Pauline Thomson had 25 years of experience in Post Offices when she moved to Matfield in Kent to become the village's sub-postmistress.
However, her business and reputation came crashing down around her when the company accused her of false accounting and theft.
Pauline told ITV News Meridian: "It was an alien world of courts, lawyers, police. I've never ever gone through anything like that. I've never been involved with anything like that. It was dreadful. Just really really dreadful."
The sum of £36,000 had gone missing from Pauline's branch.
Post Office was adamant Pauline had taken the cash, and Pauline was convicted and served a 180-hour community sentence.
She says: "I wasn't eating, I wasn't sleeping. I've never felt like that in all my life. I just really did feel suicidal. I wouldn't let them ruin my life but they've gone a good way towards it. It was 12 years ago and it feels like yesterday."
In Oxfordshire, Vipinchandra Patel was accused of stealing £75,000, and received a fine and a suspended prison sentence.
He says: "I knew if I was to stand up against them they would finish me off. So long before I went to court or went and saw the solicitor, I decided to plead guilty, otherwise I wouldn't have been able to stand up to them."
Post Office chairman Tim Parker said: “I am sincerely sorry on behalf of the Post Office for historical failings which seriously affected some postmasters.
“Post Office is resetting its relationship with postmasters with reforms that prevent such past events ever happening again.
“Post Office wishes to ensure that all postmasters entitled to claim civil compensation because of their convictions being overturned are recompensed as quickly as possible.
“Therefore, we are considering the best process for doing that.”
In addition to full co-operation with the Criminal Cases Review Commission’s review, the Post Office said it has set up an extensive disclosure exercise, by external criminal law specialists, to identify material which might affect the safety of any relevant historical prosecutions.