The meeting will last three days but it is likely the nomination will be announced next week after David Cameron gives the go ahead and Queen Elizabeth II gives her official approval.
The new leader will have a tough task ahead of him as he will be called to strengthen the unity of the Anglican community which has experienced rifts over the issue of the ordination of women bishops and gay marriage.
The favourite for the role is the 63 year old Archbishop of York, John Sentamu. If selected, he will be the first black Archbishop of Canterbury.
The 16-member Commission chaired by former British arts minister, Richard Luce, will also consider the 65 year old Bishop of London, Richard Chartes and the 61 year old Bishop of Norwich, Graham James.
Other younger candidates include the 53 year old Bishop of Coventry, Christopher Cocksworth and the 56 year old Bishop of Durham, Justin Welby.