BBC broke the news after the Archbishop's official website posted his official statement.
This is the official release in the Canterbury Archbishopric website:
Archbishop Rowan Williams has today announced his acceptance of the position of Master of Magdalene College, Cambridge with effect from January 2013. He will therefore be stepping down from the office of Archbishop of Canterbury at the end of December 2012.
Dr Williams’ intentions have been conveyed to The Queen, who is Supreme Governor of the Church of England and who formally appoints the Archbishop of Canterbury.
Dr Williams was appointed the one hundred and fourth Archbishop of Canterbury in 2002. He said today:
It has been an immense privilege to serve as Archbishop of Canterbury over the past decade, and moving on has not been an easy decision. During the time remaining there is much to do, and I ask your prayers and support in this period and beyond. I am abidingly grateful to all those friends and colleagues who have so generously supported Jane and myself in these years, and all the many diverse parishes and communities in the Church of England and the wider Anglican Communion that have brought vision, hope and excitement to my own ministry. I look forward, with that same support and inspiration, to continuing to serve the Church’s mission and witness as best I can in the years ahead.
Dr Williams will continue to carry out all the duties and responsibilities of the Archbishop of Canterbury, both for the Church of England and the Anglican Communion, until the end of the year.
The Crown Nominations Commission will consider in due course the selection of a successor.
His resignation came 6 days after meeting the Holy Father.
Did he tell the Holy Father about this? Hmmm....