Rubbina Shaheen, from Worthen, near Shrewsbury, and Tracy Felstead, from Telford, were told the news following two days of deliberations by the Criminal Cases Review Commission.
Mrs Shaheen, 54, was jailed for 12 months in 2010 for false accounting after £43,500 allegedly went missing from the Greenfields Post Office branch where she was sub-postmistress.
Miss Felstead, 37, was jailed for six months in 2001 after being convicted of stealing £11,500 from a branch in London where she was working as a counter clerk.
They are among 39 former post office workers who have had their convictions referred to the Court of Appeal. A further 22 cases are still being considered by the Commission.
Mrs Shaheen said: "It feels as if a burden has been lifted off my shoulders.
"I feel so happy, I can't explain. My name has been cleared."
Miss Felstead, who was just 19 years old at the time of her conviction said she was feeling emotional about the news.
"I have waited my whole adult life for this, it's over now, it means I can now go and move on with my life. It all feels a little bit surreal."
Miss Felstead, of Bournside Close, Brookside, was told in December that she would receive a share of a £57.75 million payout after the Post Office agreed to pay an out-of-court settlement to end a trial in the High Court.
She was one of more than 550 former post office workers who lodged a group action with the High Court claiming they had been wrongly blamed for shortfalls which had been caused by a glitch with the Post Office's Horizon database.
High Court judge Mr Justice Fraser ruled in December that a computer glitch could have led to the discrepancies.
He also wrote to the Director of Public Prosecutions Max Hill QC asking him to consider whether action should be brought against employees of computer giant Fujitsu, which developed the Horizon system. He said his concerns related to the evidence given by Fujitsu staff in previous court hearings.
The Post Office agreed to make the £57.75 million payout to bring the High Court proceedings to an end, but concerns have been expressed that most of this will go on legal costs.
Lucy Allan, MP for Telford, who described the jail terms as a 'national scandal', welcomed the news.
"This is fantastic news," she said. "The Post Office had said few, if any, would be referred.
"We're getting closer to justice thanks to so many brilliant campaigners."
Mrs Shaheen and Miss Felstead will now have to wait news of when their appeals will be held.