The answer (it’s 4 February 2013) has been placed on the Archbishop of Canterbury website.
When will Justin Welby officially become Archbishop of Canterbury?
Dr Rowan Williams, 104th Archbishop of Canterbury, stepped down from the position on 31st December 2012. Justin Welby, Bishop of Durham, was named as his successor on 9th November 2012.
Bishop Justin’s name was submitted to the Prime Minister by the Crown Nominations Commission after a consultation process to determine the needs of the diocese, the Church of England and the Anglican Communion. Consideration of the candidates took place over several months, then the Commission voted to identify a recommended candidate and a second appointable candidate. These names went forward to the Prime Minister.
In this case the recommended candidate was Justin Welby, Bishop of Durham. The Queen approved Justin Welby for election to the position of Archbishop of Canterbury, and an announcement was made by 10 Downing Street on 9th November 2012.
On 10th January 2013, the College of Canons will meet in the Chapter House of Canterbury Cathedral to elect Bishop Justin as the new Archbishop, having received a Congé d’Elire from the Crown confirming that the See of Canterbury is vacant.
A legal ceremony, the Confirmation of Election, will take place on 4th February 2013 at St Paul’s Cathedral. The Dean of Canterbury will confirm to a commission of diocesan bishops that Bishop Justin has been elected according to statute. At this point, the office of Archbishop is conferred on Justin Welby – until then he remains Bishop of Durham.
The Enthronement will take place on 21st March 2013 at Canterbury Cathedral. The new Archbishop will be placed on two thrones – the diocesan throne in the Cathedral Quire as the Bishop of the Diocese of Canterbury, and the Chair of St Augustine as Archbishop of Canterbury.