Bishop Byrne, who was appointed Auxiliary Bishop of Birmingham in 2014, will succeed Bishop Seamus Cunningham.
Speaking to Premier about his latest appointment, the Catholic bishop said he was pleased to be moving to the North East.
"I was made a Bishop five years ago and asked to serve in Birmingham and now I've been asked to serve here.
"I come here with a full heart and determined to make this my home and to serve the people of this area as best I can."
The 62-year-old becomes the fourteenth man to lead the diocese after Bishop Cunningham's held the position for ten years.
Rt Rev Robert Byrne was born in Manchester in September 1956, entered Birmingham Oratory in 1980 and was ordained to the priesthood in January 1985.
He has served as a prison chaplain for over 35 years.
Rt Rev Cunningham, who submitted his resignation after turning 75 two years ago, welcomed his successor in a statement: "I am delighted to welcome Bishop Byrne as my successor at a time of great challenge and hope in this Diocese.
"The Lord Jesus is leading us along a road of rich discernment for the future of the Church and its mission. I know that the priests, deacons, religious and people of the Diocese will warmly welcome him and assure him of our prayers."
Bishop Byrne's installation will be celebrated in St Mary's Cathedral with a service on 25th March.
Listen to Premier's Ian Britton speaking with Bishop Robert Byrne:
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