Anthony Pierce, who was Bishop of Swansea and Brecon between 1999 and 2008, has appeared at Swansea Crown Court and has admitted five counts of indecent assault on a male child under the age of 16.
The diocese Pierce served covered a large part of the county including much of Radnorshire as far north as Rhayader.
The offences Pierce admitted in court took place between 1985 and 1990, when Pierce was a parish priest in West Cross, Swansea.
The Church in Wales said the allegations came to their attention in 2023 when the survivor made a disclosure to one of their Safeguarding Officers.
It said this disclosure was immediately passed to the Police, and the Church said it worked closely with ”statutory partners as the case was investigated and prosecuted”.
Pierce has been bailed ahead of his sentencing at Swansea Crown Court, which was provisionally scheduled for March 7.
The Church in Wales revealed that an internal investigation undertaken since the 2023 report, suggests that in 1993 "a small number of members" of the Church had been aware of a further allegations against Mr Pierce, but that this was not shared with Police until 2010.
It confirmed its Safeguarding Committee has now commissioned an independent external review of the Church in Wales’s handling of this second allegation, "which will commence immediately and will be published upon completion".
The review will also consider how "safeguarding allegations are handled in the Church’s current systems" for the appointment of Archdeacons and Bishops and whether any changes to these processes are necessary.
In a statement released by the Church in Wales it said: “We acknowledge the bravery of the survivor in coming forward and thank the Police, Crown Prosecution Service and the Local Authority for their careful work in this case.
“The Church in Wales is appalled at the offences which have been revealed in this case and expresses its deepest sympathy with the victim for the abuse they have suffered.
“It is a cause of the most profound shame that a priest in the Church in Wales should have been convicted of such shocking crimes.
“Our prayers are with the survivor and with all victims of abuse, whose welfare must always be at the heart of our work.
“We hope that the manner with which the disclosure was handled when it came to light in 2023 will give confidence that the Church is serious about dealing firmly and decisively with any such cases.”
“If our people and processes have failed victims and survivors of abuse in the past, we intend to take responsibility for that fact and to fully apply the lessons which have been learned.”
Following sentencing in the criminal court next month, the Church in Wales has said its Disciplinary Tribunal will consider further appropriate action.