White is currently priest-in-charge of Riding Mill in the Diocese of Newcastle.
She is married to Bishop Frank White, Assistant Bishop of Newcastle. The couple have family in England and South Africa.
Announcing the news, the Archbishop of York Dr John 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." White said she was "absolutely amazed" by the news.
She said: "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. "It feels like a wonderful gift It's going to be a huge adventure.
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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.
White replaces the Right Rev Richard Frith, who became Bishop of Hereford in November 2014.
She will be consecrated at York Minster in July.
The 58-year-old became a priest in 1996 and has served in Durham, Sheffield, Peterborough and Newcastle.