The responsibility for choosing the next Archbishop of Canterbury rests with a special commission. It submits the name of its preferred candidate to the Prime Minister who then submits the advice to the Queen. You can read the procedure in full here.
Dr Rowan Williams has accepted the position of Master of Magdalene College, Cambridge with effect from January 2013.
Archbishop Rowan Williams will be stepping down from the office of Archbishop of Canterbury at the end of December 2012.