The 48 year old will move from his current role as suffragan Bishop of Dudley, in which he has served since 2014.
He replaces namesake Rt Rev Graham James who stepped down in February.
Speaking about his new role, he said: "It's a great honour and somewhat daunting to be nominated as Bishop of Norwich. I'm excited to have been called to serve among the people of Norfolk and Waveney as together we seek to live out Jesus Christ's call to love God and our neighbours.
"A theme of God's calling in my life is that each new chapter has been to a new and unexpected place. The Diocese of Norwich is equally a new and unexpected place for me, and what a wonderful privilege it is to be called to serve here.
"I see the role of a bishop as encouraging others to live out their faith in Jesus Christ with a generosity of spirit and compassion, bringing people together to serve their neighbours in partnership with others."
Bishop Graham was ordained as a priest in 1997. Before moving to the midlands he served in the north east of England.
He's an honorary canon at St Cyprian's Cathedral in Kumasi, Ghana and has a keen interest in ecology.
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