Lord Hope of Thornes was Archbishop of York for ten years, from 1995 to 2005. It was during this time that allegations were brought to him that the late Robert Waddington, a former dean of Manchester Cathedral, was sexually abusing children.
Lord Hope did not refer the accusations against Mr Waddington to the police or child protection agencies. Instead, he revoked Waddington's right to conduct church services.
The independent report was commissioned by the current Archbishop of York Dr John Sentamu and led by Judge Sally Cahill QC.
It accused Lord Hope of putting the interests of Mr Waddington above those of the victims, and says because of the way he acted the chance to prosecute Waddington before he died in 2007 was missed.
There were also "systemic failures" into the way the Church of England handled allegations of child abuse in this particular scenario, according to the report.
In a statement, Lord Hope said: "After much prayerful and considered thought I wrote at the beginning of the week to the Bishop of Leeds and in the light of the Cahill Inquiry Report I have submitted my resignation as Honorary Assistant Bishop of Bradford, now West Yorkshire and the Dales, with immediate effect.
"This ends my nearly 50 years of formal ministry in the Church of England, which I have always sought to serve with dedication. I will certainly continue to pray for the important ongoing work with survivors."