Canon Dyer said she was "delighted to be elected" and added: "It will be a privilege to lead the people of this diocese as they continue to make known the love of God to those in their communities and beyond.
"I am looking forward to both the challenge and excitement of serving and worshipping together in diverse locations across the diocese and to joining the College of Bishops."
The General Synod of the Scottish Episcopal Church voted to allow the election of female bishops in 2003 but no female appointments have been made in the following 14 years.
The See of Aberdeen & Orkney became vacant last November when the Rt Rev Dr Robert Gillies retired as bishop of the Diocese.
Most Rev Mark Strange, Bishop of Moray, Ross & Caithness and Primus of the Scottish Episcopal Church said; "Anne brings with her a wealth of experience in theological education and mission development, and has so many of the gifts sought by the diocese together with a deeply loving and generous personality.
"I am also delighted that those gifts have allowed us to elect a woman to our College of Bishops. Please pray for Anne, her family, for the congregation at Haddington and for the Diocese of Aberdeen & Orkney as they journey on in faith."
Canon Dyer has been the rector of Holy Trinity church, Haddington since 2011. Her wider church involvement includes being a member of the Scottish Episcopal Institute Council and a member of General Synod.
Being in the first group of women for each of these Orders, Canon Dyer was ordained Deacon in 1987 and Priest in 1994 in Rochester.
She served as Warden of Cranmer Hall, Durham and before that was Ministry Development Officer in the Diocese of Rochester.
Prior to ordination Anne Dyer read Chemistry at St Anne's College, Oxford and was a Business Systems Analyst with Unilever before training for ordained ministry at Wycliffe Hall, Oxford and studying theology at King's College London.
