From the Archbishop of Canterbury’s website.
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