Leslie Horobin and Kevin Wilcox, who were sentenced at Wolverhampton Crown Court in December 1986, claimed their confession statements were falsified. Their initial appeals were rejected in 1988.
The case was referred back to the Court of Appeal by the Home Secretary and the Crown conceded it could no longer rely on the confession evidence.
Mr Horobin, 41, and Mr Wilcox, 35, both from the Walsall area, did not give evidence at their trial when they were convicted of a pounds 100,000 Post Office van robbery. The Crown's case had rested on unsigned confession evidence. The appeal court will give its reasons for allowing the appeal at a later date.