Very Rev Vivienne Faull, who is currently the Dean of York, will be officially welcomed into the role during a service at Bristol Cathedral in the autumn.
Commenting on the appointment, she said: "This is where my family comes from, and so coming here feels like I am returning home."
Brought up in a rural area of the Wirral, Very Rev Faull previously worked with the Church Mission Society in northern India as a teacher and also served as a youth worker in Everton.
She continued: "It was 24 years ago that Bristol was the first diocese to ordain women as priests, and I want the Diocese to continue to show that pioneering courage.
"I look forward to leading a church that shows the love of Christ to everyone, whoever they are."
Very Rev Faull trained for ministry at Saint John's College in Nottingham and Nottingham University, before becoming an ordained priest in 1994.
She is married to Michael, a hospital consultant.
Archbishop of York, Most Rev John Sentamu, said: "I rejoice with the Diocese of Bristol that Her Majesty the Queen has accepted the nomination of the Dean of York, the Very Revd Vivienne Faull, to be the 57th Bishop of Bristol.
"Dean Faull leads by following Jesus' way with insight and oversight, with a readiness to be led as well as to lead.
"She has been a great Dean for York, taking risks for the Kingdom of God, for example persuading the Dean and Chapter to put on the Mystery Plays inside the Minster."
Very Rev Faull's mother was brought up in Bristol by parents who lived in the city all of their lives.
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