The service will be held next Friday morning by GAFCON at Edman Chapel on the campus of Wheaton College, near Chicago.
The group of conservative Anglicans created the post in reaction to a move by the Scottish Episcopal Church (SEC) last June towards allowing same-sex marriage. The Church officially approved the step earlier this month.
GAFCON accused the SEC of joining the Episcopal Church (USA) and the Anglican Church of Canada in "rejecting the authority of the Bible".
It said the introduction of a new Missionary Bishop for Europe recognises "the pastoral need" for "faithful Anglicans" which arose following the initial SEC vote. GAFCON hopes the new bishop will "plant dynamic churches all over Scotland".
The appointment, which was done without the blessing of the Church of England, prompted a rebuke by the Archbishop of Canterbury.
Most Rev Justin Welby warned against African Anglican leaders against creating "disturbance and discords" by intervening in Britain.
In a letter to fellow Anglican leaders - obtained by the Mail on Sunday - Archbishop Justin accused them of a "cross-border" intervention that would "carry no weight in the Church of England".