Most Revd Justin Welby reportedly made the promise during a private meeting with survivors at Lambeth Palace earlier this week.
The Archbishop has been under pressure to act in the wake of a decision earlier this year by the Methodist Church to publicly apologise to abuse victims, after its own independent investigation uncovered reports of nearly two thousand alleged abusers, including 914 allegations involving sexual abuse.
"It's very brave and the right thing to do. The Church has got a problem and therefore the leadership has got to take a firm and robust stand," said General Synod member Revd Canon Jonathan Ford to Premier.
As we know we know from our experience of our Roman Catholic brothers and sisters, because the church of Rome refused to deal with this 20 to 25 years ago it actually turned out to be far worse, so I think it's very brave and the right thing to do to publicly identify that abusers have nowhere to hide in the Church of England," added Canon Ford.
On Thursday, Government inquiry chair Judge Lowell Goddard warned that bishops and other faith leaders will face 'difficult' questions as she formally opened the investigation into allegations involving public bodies or officials, including claims of an historical Westminster paedophile ring.
It won't have the power to convict anyone, or award compensation, but can name people who've abused children.
Meanwhile, the Archbishop of York has raised concerns over a loophole in ecclesiastical law which he said could allow convicted paedophile priests back into ministry.
Dr John Sentamu warned members of the General Synod on Saturday that even he has no power to demand to see the files of banned clerics from other dioceses who retire to his area and apply for a new permission to serve as a priest again.
The Archbishop raised his concerns as Synod members passed a raft of new safeguarding polices which include new rules making it easier to suspend a cleric accused of abuse and end the time limit on bringing allegations against clergy in sexual cases.
But Dr Sentamu warned that unless the issue he raised was dealt with, abusers could return to serve as priests in a different part of England and potentially reoffend.
Dr Sentamu told of two separate cases where retired priests banned from ministry elsewhere had applied to him for PTO [Permission To Officiate] but refused to take part in a risk assessment.