The announcement comes after the selection of a previous candidate, Bishop of Burnley Rt Rev Philip North, prompted a backlash over his opposition to appointing female clergy.
Speaking about the latest announcement, Bishop Philip North said: "I am overjoyed to hear the news that Pete Wilcox is to be the next Bishop of Sheffield, a priest whose ministry I have long admired.
"I pray that clergy and laypeople of all traditions will be able to unite around his leadership and so together continue to bring renewal to the Parishes of the Diocese to the glory of God."
Last month, Bishop Philip announced with "great regret and sadness" he was refusing the nomination, one day after Sheffield MP Louise Haigh branded his views on women bishops "troubling".
Commenting on his own appointment, Dr Pete said: "Although the journey has been unconventional, to say the least, I feel called by God to this role and am therefore thrilled to be coming to the Diocese of Sheffield.
"There will be much for me to learn, but I am excited about the work which is already underway to share the good news about Jesus, and to work for the justice and peace which the kingdom of God will bring."
Dr Pete, who is 55 and has been ordained for more than 25 years, has previously served at churches in Gateshead and Walsall before becoming Canon Chancellor at Lichfield Cathedral.
Archbishop of York Dr John Sentamu said: "The nomination of The Very Reverend Dr Pete Wilcox, Dean of Liverpool, as the 8th Bishop of Sheffield will take the Diocese forward in its evangelistic and mission opportunities for the peoples of the Diocese of Sheffield.
He added: "He is a gifted and renowned Bible teacher, pastor and enthusiastic evangelist. He is totally committed to social justice and human flourishing."
Addressing the recent controversy in the Diocese with the withdrawal of Bishop Philip, Dr Pete said: "No-one I've spoken to has been able to think of any other occasion when a newly announced diocesan bishop has been, as a matter of public record, not the first choice. You might be wondering how that feels. And my honest answer is, it feels fine, actually."
Listen to Dr Pete Wilcox speaking to Premier's Marcus Jones: