This came nine years after a 1975 inquiry led to him being banned from doing so. Cardinal Sean Brady, then a priest, participated in that inquiry.
According to a statement issued to RTÉ News this evening by the current Bishop of the diocese, Dr Leo O'Reilly, in 1984 Smyth asked the then Bishop, the late Dr Francis MacKiernan, to lift the ban.
Following consultations with the then Abbott of Smyth's monastery, Bishop MacKiernan acceded to Smyth's request.
The statement adds that, at first, permission to return to hearing confessions and celebrating Mass publicly in the diocese was given for periods of six months at a time.
Three years later, the period was extended to 12 months.
Permission was renewed each subsequent year until it was finally withdrawn in 1993 when Bishop MacKiernan learned that the DPP in Northern Ireland was bringing a criminal prosecution against Smyth.
Cardinal Brady ceased to be Bishop McKiernan's Secretary five years before the decision to allow Smyth to return to full public ministry.
It was in his roles as Bishop's Secretary and as a Church lawyer that he participated in the 1975 inquiry