But the Most Rev Justin Welby said conditions to him accepting the role “have not yet been met”.
He told MPs they must not attempt to use a public forum as a way of attempting to stop Brexit.
He said: “It is an unexpected privilege to be asked to chair this proposed citizens’ forum on Brexit.
“In the past this kind of gathering has, in many places and in difficult situations, opened the way for careful deliberation if at the right time and genuinely representative.
“I am honoured to be approached and would be willing to accept in principle, subject to some conditions which have not yet been met.”
Mr Welby said any such forum “should not be a Trojan horse intended to delay or prevent Brexit in any particular form”.
He also said any citizens’ forum should have cross-party support and “time to be properly organised”.
A cross-party group of senior MPs, including Labour’s Yvette Cooper and Conservative Dame Caroline Spelman, formally asked the Church of England’s most senior cleric to chair a citizens’ forum on Brexit on Tuesday.
They suggested such a forum – where members of the public with differing views on Brexit and from a host of backgrounds and demographics would discuss the way forward on Britain’s exit from the European Union – could “help the whole country”.
In their letter, the MPs said any forum should meet before Britain’s exit deadline on October 31 and that further meetings would be required.
The Times had earlier reported MPs were in talks with Mr Welby, with plans in place for the forum to meet at Coventry Cathedral next month.
The MPs, including a Brexiteer, went public with the move, publishing their letter formally asking the archbishop to conduct proceedings following a meeting on Tuesday of key Commons figures opposed to a no-deal Brexit.
The letter was signed by Labour MPs Hilary Benn and Ms Cooper, Liberal Democrat Norman Lamb, the SNP’s Angus MacNeil, Dame Caroline, and independent member Frank Field. All but veteran MP Mr Field are pro-EU politicians.
The MPs wrote: “Given the polarisation we have all experienced across the UK and within Parliament, we believe that a citizens’ forum on Brexit would be an opportunity to consider how to heal the divisions in our country since the Brexit referendum.
“We are writing to ask if you would be willing to oversee such a process.
“The forum would benefit greatly if you were willing to chair an independent panel that reflects the diversity of views throughout the UK to oversee the forum and ensure it is fairly run, and to work with other partners to see if it is possible to make such a forum happen.
“A process which involves a bit less shouting and a bit more listening and considering could help the whole country.”
The citizens’ forum model has been used in the UK previously to seek solutions for social care, and was successfully used in Ireland when preparing the wording of the referendum question last year on whether to legalise abortion.
The archbishop received support from fellow clergyman the Bishop of Buckingham.
The Right Rev Alan Wilson said: “In a mature democracy people would not be afraid of doing this, because it would show what people’s concerns and fears and hopes and aspirations around this subject were.”