The Episcopal Electoral College for Meath and Kildare elected Archdeacon Stevenson at a meeting in Christ Church Cathedral, Dublin, yesterday.
He succeeds the Most Rev Dr Richard Clarke, who became Archbishop of Armagh and Primate of All-Ireland in December.
Archdeacon Stevenson (53) is the rector of Portarlington (Kildare) and has been Archdeacon of Meath and Kildare since 2009.
In a statement, he said: “I have served in Meath and Kildare for over 13 years and enjoyed a very happy working relationship with the now Primate of All Ireland, Archbishop Clarke. Now I am about to serve the diocese in a new way as bishop. I am looking forward to working in a rural diocese which I have come to know so well and to the challenges and opportunities which lie ahead as well as making a contribution to civic life. I also look forward to working with my fellow bishops in due course.”
Following approval by the House of Bishops, the bishop-elect will be consecrated on a date to be determined.
Archdeacon Stevenson was educated at the University of Ulster, the Church of Ireland Theological College (now Institute) and at the Irish School of Ecumenics, and was ordained deacon in 1983 and priest in 1984.
He served two curacies in the Diocese of Down before becoming Rector of Donaghadee (Down) in 1992.