White will become the Church's of England's second female bishop at a ceremony on July 3 in York, the diocese which includes Hull.
"This is an adventure I had never imagined setting out on," White said in a statement.
"You may have noticed that I am married to a bishop. This may seem excessive! You would think that one in a family is more than enough.
"Believe me, this has crossed our minds."
Her husband, Frank White, is a deputy bishop in Newcastle in northern England although in effect he has the same status as a bishop.
The Archbishop of York John Sentamu, who made the announcement, said it was "a joyous day".
"Alison is a person of real godliness and wisdom -- it is fantastic that she has accepted God's call," he said.
The Church of England consecrated its first female bishop, Libby Lane, in January.
The general synod of the Church of England last year gave final approval to a historic reform allowing female bishops.
Women have been able to be ordained as priests in England since 1992 and now make up a third of the clergy.