Retired clergyman Granville Gibson, 79, was found guilty after a trial at Durham Crown Court of two counts of indecent assault, dating back to the late 1970s.
He quickly rose through the clergy in the Diocese of Durham to become Archdeacon of Auckland before his retirement.
A jury cleared him of five other charges.
The Diocese of Durham confirmed a full and independent review of the circumstances surrounding the case had been launched.
In a statement the Bishop of Durham Rt Rev Paul Butler said: "Following the conviction today of the Venerable Granville Gibson on two charges of indecent assault, we offer an unreserved apology to all the survivors and those affected by this news.
"We commend the bravery of those who brought these allegations forward, acknowledging how difficult and distressing this would have been.
"We are profoundly sorry for the abuse perpetrated by Mr Gibson and remain committed to doing everything possible to ensure the well-being of children, young people and adults, who look to us for respect and care.
"Abuse is a terrible crime and a grievous breach of trust, which has lifelong effects."
He added that his prayers were with everyone involved and that anyone with safeguarding concerns should contact officials.