The 60-year-old’s DNA was linked to the crimes after he was cautioned for urinating on a neighbour’s plant pot.
His family says Thomas McKenna was the rapist and has won permission for the exhumation from the Church of England.
Eric McKenna’s wife Moira petitioned the CofE to allow the exhumation to take place. Her husband has always denied he carried out the street attacks.
His father Thomas McKenna, who died in 1993, is buried in St John’s cemetery in the Elswick area of Newcastle.
A spokesman for the Diocese of Newcastle said: “The Church of England will only grant permission to exhume a person’s remains from consecrated ground in exceptional circumstances.
“Recent cases considered by the Consistory Court have laid out principles that each chancellor should follow when considering an application for exhumation.
“Our chancellor Euan Duff has followed these principles when considering this case, although he has been very clear that granting permission in no way supports the accusation being made against the deceased.
“It is recognition that the DNA analysis may help settle this matter once and for all.”
Following the conviction last year, Det Con Mick Wilson of Northumbria Police said: “McKenna thought he had got away with his crimes, but a neighbourly dispute and a moment of stupidity has landed him in prison for 23 years.”
After the case, the Crown Prosecution Service said the chance of Eric McKenna not being the source of DNA samples recovered at the two rape scenes was one in one billion.
Northumbria Police has been approached for comment.