Bishop Wilson has been the Auxiliary Bishop of Westminster since 2015 and was previously a priest in the Diocese of Leeds.
He will succeed Most Rev Peter Smith, who has been Archbishop of Southwark since 2010.
Speaking of his appointment, the Archbishop-elect said: "Someone once said if you want to make God laugh, tell him your plans.
"In whatever way I might have imagined God's plan for my life to unfold, the news of my appointment by Pope Francis as the new Archbishop of Southwark came as a complete surprise.
"I am grateful to His Excellency Archbishop Edward J Adams, the Apostolic Nuncio, for his encouragement, and for reminding me of C S Lewis' invitation to be 'surprised by joy.'
"It is the joy of the Gospel, the Good News of God's love for the world in His Son Jesus Christ that sustains and animates the Church's mission in which I am to share in a new way."
Archbishop Smith said he was "pleased to pass on my responsibilities to such a capable successor".
His words were echoed by Cardinal Vincent Nichols, Archbishop of Westminster who said: "On behalf of the people, priests and religious of Westminster I assure Archbishop-elect Wilson of our whole-hearted support and prayers as he moves to take up his role as Archbishop of Southwark.
"We thank him most warmly for his service in Westminster both as an area bishop and a dedicated part of episcopal oversight of the Archdiocese, especially in education."
Archbishop Elect John Wilson was born on 4th July 1968 in Sheffield. He studied for a Bachelor of Arts degree in theology and religious studies at the University of Leeds and began formation for the priesthood for the Diocese of Leeds at the Venerable English College, Rome in 1989.
He was ordained a deacon on 13th July 1994 and ordained to the priesthood on 29th July 1995.
In 2005, he was appointed Episcopal Vicar for Evangelisation in the Diocese of Leeds and held this position until 2012. From 2008 to 2014 he was also sessional chaplain at HMP Leeds and in 2011 he was named a Chaplain to His Holiness by Pope Benedict XVI.
From 2015 to 2016 he served as Parish Priest of St Martin de Porres, Wakefield.
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