Richard Ormerod, 79, and Gillian Harrison, 69, had both been convicted of fraud charges based on evidence from the Post Office's faulty IT system.
Their convictions were quashed at Southwark Crown Court with no opposition to their appeals.
The Post Office said it was sorry for "historical failings".
Mr Ormerod, who worked at the Summerhouse Post Office near Darlington, was sentenced to a 12-month conditional discharge and ordered to pay £250 costs after pleading guilty to three charges of fraud by false accounting relating to a £31,097 shortfall in the branch accounts in 2004.
Mrs Harrison pleaded guilty at Newcastle under Lyme Magistrates' Court in Staffordshire to four offences in relation to an alleged cash shortfall of £1,474 at her Post Office in Dresden, Stoke-on-Trent, in 2005 and was sentenced to a 12-month rehabilitation order and ordered to pay £1,474 compensation plus £320 costs.
Despite their guilty pleas, both had consistently denied taking any money and, at the latest hearing on Thursday, Judge Deborah Taylor allowed their appeals.
"The convictions are quashed," she said, adding: "Both Mr Ormerod and Mrs Harrison have been of good character throughout. It is a recognition and a public exoneration of you."
Mr Ormerod thanked the judge, while Mrs Harrison burst into tears, as the pair were supported by loved ones in the public gallery.
Graeme Hall, representing the appellants, said the convictions had "plagued their lives for many years".
Mrs Harrison said the ordeal had "destroyed" her life and those of her family, but that she now wanted to look to the future and encourage others who were wrongly convicted to get justice.
"I think the Post Office is diseased and it needs eradicating," she said, adding: "I just want people to come forward. It is important."
Mr Ormerod said he could not believe that the hundreds of sub-postmasters convicted were all guilty and that it must have been the Horizon system all along.
"They were so heavy-handed at the top end, and they couldn't bear to face the truth," he said, adding: "Nothing will happen to them, they have just been allowed to carry on."
Simon Baker QC, representing the Post Office, said: "Both are cases in which the convictions were predicated upon the Horizon computer system with which the court is now familiar."
A Post Office spokesman said it had "undertaken fundamental reforms" and was "sincerely sorry for the impact of historical failures on the lives of the people affected".