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 Post Office's abandoned underground railway opens its doors on Friday some 14 years after the last letter was transported through it.
Drinking alcohol most days of the week can significantly protect against developing diabetes, a study has found.
Philip Hammond wants to maintain full access to the European single market and customs union in a transitional Brexit deal, say reports.