Nick Baines helpfully reproduces for us the process by which a person becomes the Archbishop of Canterbury (scroll down near to the bottom). Note these two steps:
Once the Queen has approved the chosen candidate and he has indicated a willingness to serve, 10 Downing St announces the name of the Archbishop-designate.
The College of Canons of Canterbury Cathedral formally elect the new Archbishop of Canterbury.
Did you get that piece of ridiculousness? If not, Bosco Peters will explain it for you:
After the Queen receives the name from the Prime Minister she passes it to the Canterbury’s College of Canons. They meet to “elect” the new Archbishop of Canterbury. Ralph Waldo Emerson wrote about this:
The King sends the Dean and Canons a congé d’élire, or leave to elect, but also sends them the name of the person whom they are to elect. They go into the Cathedral, chant and pray; and after these invocations invariably find that the dictates of the Holy Ghost agree with the recommendation of the King [Emerson, English Traits, XIII, 1856]
As the late Bishop Stephen Neill wrote in his book ‘Anglicanism’:
It is a happy thing that all the other Anglican Provinces have freed themselves from the past, and that it is only on the forty-three dioceses of the English provinces that the hand of Henry VIII still rests so heavily.