The current Dead of Liverpool, the Very Reverend Dr Pete Wilcox, said: "He will make an excellent leader of the Anglican Communion.
"The cathedral greatly benefited from his inspired leadership during his four years here, and in that time he undoubtedly gained the respect of colleagues and congregations alike.
"It’s an appointment which reflects well on the Diocese and City of Liverpool, and there is great confidence here that the skills and qualities he displayed as Dean will stand him in good stead in the challenges he will face in his new role.
"Our prayers are with Justin, Caroline and all the family as they embark on their new phase of ministry and with the people of the Diocese of Durham as they adapt to his departure."
More top news
Manchester City have signed Australia international midfielder Aaron Mooy from sister club Melbourne City.
A new campaign to stop young people in care being moved out of their local community
Wallasey MP Angela Eagle is set to challenge Jeremy Corbyn for the Labour leadership, ITV News understands.