Despite not being appointed with the blessing of church officials here, Rev Canon Andy Lines said he had accepted the new role because it is a "logical next step".
Speaking on the divide within the Anglican Communion his appointment could cause, he told Premier: "I think that actually the people who should have worried about that are the people who've made the decision today in the Scottish Episcopal Church because they're the ones who are moving away.
"I am staying where the Anglican Communion has always been in its beliefs."
The Scottish Episcopal Church recently voted in favour of allowing same-sex couples to be allowed to marry in church, putting it at odds with the majority of the global Anglican Communion.
GAFCON, a worldwide group of conservative Anglicans, named the English based Rev as a missionary bishop to cater for disaffected Christians in Scotland, England and across Europe.
Most Rev Dr Foley Beach, Archbishop of the Anglican Church in North America said the group's concerns had been ignored for years. He told Premier: "In our last meeting we decided 'enough is enough' - it's time to provide some help.
"The sheep are suffering and it's time to provide leadership and guidance and help."
Speaking on the importance of the new appointment he said: "Many of our GAFCON primates and people that they serve would wonder if this is even Christianity any more - the things that are being taught. Its not just about sexuality issues - its basic theology.
He said they wanted to provide help to those in the Anglican community that want to "remain true to their historic faith."
"Many have chosen not to associate with us because of our stance but really they're the ones causing division - we're not causing division," he added.
Same sex marriage became legal in Scotland in the end of 2014, despite opposition from the Church of Scotland and Roman Catholic Church.
Synod last year ruled that the issue of same-sex couples being unable to be married in church should be discussed across its seven dioceses. Six voted in favour of changing the law, with only Aberdeen and Orkney opposing.
Rev Dave McCarthy, coordinator of the Scottish Anglican Network told Premier how he feels about the appointment: "I'm sad that we've reached the point of doing this.
"We hoped and prayed that this wouldn't be the case - that we wouldn't have to look for alternative care and it's heart-breaking.
"But it gives us an option of care and authority."
A similar appointment in the USA in the 2000's led to a formal split in the US Episcopal Church.
GAFCON says although the Anglican Church in North America is the consecrating Province, this is an initiative of the wider Anglican Communion.
Listen to Rev Canon Andy Lines speaking with Premier's Ian Britton:
Listen to Most Rev Dr Foley Beach speaking with Premier's Ian Britton:
Listen to Rev Dave McCarthy speaking with Premier's Ian Britton:
