The Archbishop of Canterbury must fulfil a number of roles including that of bishop of the Canterbury diocese and head of the Church of England as well as acting as a "focus of unity" for the worldwide Anglican Communion.
In recent years, the Anglican Communion has been split by the divide between traditionalists and liberals over homosexuality.
The appointment comes as the CoE General Synod stands poised to give final approval in November to the introduction of women bishops after years of negotiations.
Dr Williams has described the post of Archbishop of Canterbury as one of "immense demands" and has said his successor will need the "constitution of an ox and the skin of a rhinoceros".
More top news
The Tories' Brexit civil war will rear its ugly head again soon enough.
Watchdog says officers must work harder to avoid the use of force on mentally unwell people in a report into the death in custody.
Morning wind and rain in Scotland and western England will move eastwards, leaving brighter weather behind it by late afternoon.