The new Bishop of Hull will be the Reverend Canon Alison White, the Archbishop of York Dr John Sentamu has announced.
Mrs White is currently priest-in-charge of Riding Mill in the Diocese of Newcastle.
Dr Sentamu said: "This is a joyous day. I am delighted to be welcoming Alison as the next Bishop of Hull. She's a very gifted person."
Mrs White said she was "absolutely amazed" by the news.
"It's been a long time in coming and so many people have prayed, hoped and thought about the way God is taking this into the future," she said.
"It feels like a wonderful gift. It's going to be a huge adventure.
"Hull's got a great story. I love that video that was done in support of its bid to be City of Culture. What a wonderful time to be coming in as Bishop of Hull, it couldn't be better."
The Church of England's first woman bishop is The Rt Rev Libby Lane, who was consecrated as the eighth Bishop of Stockport at York Minster in January.
Mrs White replaces the Right Rev Richard Frith, who became Bishop of Hereford in November 2014.
She will be consecrated at York Minster on 3 July.
The 58-year-old became a priest in 1996 and has served in Durham, Sheffield, Peterborough and Newcastle.
She is married to Bishop Frank White, Assistant Bishop of Newcastle. The couple have family in England and South Africa.
The Church's General Synod formally approved plans in November to ordain women bishops after years of division and in the face of stiff opposition.
Frank and Alison White - or Mr and Mrs Bishop, as they will be - are the first married couple who'll both serve as bishops in the Church of England. Welcoming her appointment, the Archbishop of York said his first reaction was simple: "Yippee! She has great people skills."
The Whites met in 1980 and married in 1982, and Canon Alison White says that even as bishops, "we are first and foremost Frank and Alison - we've been married for over 30 years now."
Both finish each other's sentences, and Frank adds that they are great friends and "I think we'll learn from one another and share stories along the way." They're relieved that they can now share the news with friends and family, having known about the appointment for several weeks.
Asked if there is any rivalry between them, both shake their heads in unison. Bishop Frank White is a Newcastle United supporter, and has spent years trying to persuade his wife that football is a good thing - and hopes she will now become a great supporter of Hull City.
Alison pays tribute to the work of Libby Lane, the first woman to be appointed as a bishop in the Church of England. She says that having two bishops in one family may seem excessive, but that it is their marriage that's sustained both her and her husband Frank, as well as their shared vocation - even if her new appointment means they'll both be busier than ever.
A second woman has been appointed a bishop by the Church of England.