A number of archbishops and bishops were present for the consecration of Rev Canon Andy Lines.
GAFCON, a group of conservative Anglicans created the new 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 year.
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".
Friday's consecration service concluded the "Mission on Our Doorstep" conference which has drawn over 1,400 Anglican leaders from around North America and the world.