The position is being created by the Global Anglican Futures Conference (GAFCON), an international group of conservative Anglicans who believe marriage is intended to be a life-long union solely between one man and one woman.
GAFCON said the new bishop will minister to churches who have rejected the Church of England "for reasons of conscience".
In a statement, the group said: "...within England there are churches that have, for reasons of conscience, been planted outside of the Church of England by the Anglican Mission in England (AMiE).
"These churches are growing, and are in need of episcopal leadership.
"Therefore, we have decided to consecrate a missionary bishop who will be tasked with providing episcopal leadership for those who are outside the structures of any Anglican province, especially in Europe."
The decision comes after the organisation previously warned of a "troubling ambiguity from diocese to diocese" in the Church of England on teaching and pastoral practise concerning sexuality.
In February, LGBT campaigners welcomed a decision by the Church of England's governing body to reject the House of Bishops which advised that teaching on marriage should consider it a union between one man and one woman.
The announcement, which followed a meeting of GAFCON leaders in Nigeria last week, also came after the organisation raised "immediate concern" over plans by the Scottish Episcopal Church to approve in full gay marriage next month.
In the statement, GAFCON said: "During our meeting, we considered how best to respond to the voice of faithful Anglicans in some parts of the Global North who are in need of biblically faithful episcopal leadership.
"Of immediate concern is the reality that on 8th June 2017 the Scottish Episcopal Church is likely to formalize their rejection of Jesus' teaching on marriage.
"If this were to happen, faithful Anglicans in Scotland will need appropriate pastoral care."
AMiE said: "AMiE are delighted that the GAFCON Primates have given their support for the consecration of a Missionary Bishop.
"We thank God that the number of AMiE churches is growing and that an increasing number of individuals are exploring ordination with us.
"As a result, we have an urgent need for more episcopal leadership."