The Rt Revd Christopher Chessun was 'elected' as Southwark's next bishop by the cathedral's College of Canons at an election court on Thursday.
The appointment of the current Bishop of Woolwich as Southwark's next diocesan bishop was announced by Downing Street last month.
Thursday's ceremony in the cathedral's retrochoir was part of a series of legal formalities that must be observed before the bishop can begin his new ministry.
The election court, presided over by Canon Andrew Nunn, Sub-Dean of Southwark Cathedral, and the diocesan registrar Paul Morris, required all those present to acclaim that they wish Bishop Christopher to be their new bishop.
The election of the bishop now has to be confirmed and this will take place in the Court of Arches on Monday 17 January.
At that stage Bishop Christopher legally becomes the Bishop of Southwark although he will not take up his public ministry until he is enthroned at Southwark Cathedral in early 2011.