Letters from 1966 between the then Archbishop of Canterbury and a bishop show the Church agreed that a convicted paedophile should be ordained.
The correspondence has emerged in a report into the Church's failure to support victims of Roy Cotton that was published online and then removed.
In one letter, Lambeth Palace suggested Cotton should be placed in a "carefully selected parish".
Lambeth Palace said robust safeguarding policies had been in place since 1995.
The Meekings Report was published online on Wednesday and then taken down. At the same time, another report was released by Baroness Butler-Sloss.
A spokeswoman for the Diocese of Chichester told the BBC the Meekings Report was removed because the document had accidentally included some confidential information.
Both studies looked into the behaviour of Cotton and another paedophile priest, Colin Pritchard.
In a letter to the then Archbishop of Canterbury Michael Ramsey dated 13 May 1966, the Bishop of Portsmouth outlined Cotton's history, including a criminal offence in 1954, and his repeated requests to be considered for ordination.
It said: "At the time he protested his innocence, and he has done ever since, and in fact from that time has been teaching."
The letter continued: "I am not sure whether having been convicted there would need to be a dispensation from you and I would be most grateful for your guidance in this matter.
"Cotton is a man of considerable ability... and I cannot think that having been so free of any trouble for 12 years that there is a likelihood of there being any problem in the future."
A response from the archbishop's secretary dated 17 May 1966, said the archbishop was "reassured by what you have said and thinks you would do right to consider ordaining him to a title in the carefully selected parish which you mention".
On Wednesday, the Church-commissioned report by Baroness Butler-Sloss criticised both senior clergy and Sussex Police over how they dealt with historical claims of abuse by Cotton and Pritchard.
In the report, she said across the diocese "and probably in many other dioceses" there had been "a lack of understanding of the seriousness of historic child abuse".
She said the victims' claims were not taken seriously.
The Bishop of Chichester later apologised, while Sussex Police issued a statement saying the force had always taken claims of sexual abuse very seriously.
The retired senior judge also said she believed Roy Cotton had at least 10 victims.
Pritchard served as the vicar of St Barnabas, Bexhill, until 2007 after being arrested over sex abuse claims. In 2008 he pleaded guilty to sexually abusing two boys in the 70s and 80s and was jailed for five years.
The offences took place while he was parish priest at St Andrew's Church in Wellingborough, Northamptonshire.
The court heard that Cotton had been involved in the offences but died in 2006, two weeks before Pritchard was arrested. Cotton worked as a priest in Brede, near Rye, in the 1990s.
A statement from Lambeth Palace in response to the Meekings Report said: "We would never comment on details of individual cases but always take the line that one safeguarding case in the Church of England is one too many and since 1995 have robust safeguarding policies in place.
"The Church of England takes all safeguarding issues and allegations very seriously and the Butler-Sloss review for Chichester Diocese is an example of this.
"We continue to stress that anyone who has any information or concerns about the suitability of anyone working with children today within a church setting should share those concerns with the relevant diocesan child protection adviser, or the police or social services.
"The safeguarding of children and vulnerable adults in our care is central to all our activities and any case of harm that occurs is a source of deep regret and pain."