He was named on a short list for the role in April earlier this year.
The job has instead gone to Very Rev Andrew Swift who moves from the Diocese of Argyll & the Isles.
Dr Jeffrey John was nominated as Bishop of Reading 15 years ago but stood aside after the then Archbishop of Canterbury Dr Rowan Williams asked him to withdraw from the process in order to avoid a church split.
Reports since suggest he's been put forward a number of times for a role as a bishop but has yet to be successful. Last year his nomination as Bishop of Llandaff was blocked by Welsh bishops.
Jeffrey John entered into a civil partnership with Grant Holmes in 2006 after a 30 year relationship. They have stated their relationship is celibate.
Speaking about his appointment, Very Rev Andrew Swift said: "It is a wonderful and humbling honour to be elected as the next Bishop of Brechin.
"I would like to thank the electoral synod for their trust in me, and look forward very much to working with all the Scottish Episcopal Churches of Brechin to help them build up their confidence, witness and mission in Dundee, Angus, the Mearns and Carse of Gowrie.
"I am also praying for my fellow candidates in the election - thanks and blessings for them all."
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