He takes over from Archbishop Dermot Clifford who retired due to his age.
The Holy Father made the announcement at the Vatican this morning.
He was made a bishop by Pope Emeritus Benedict XVI in 2010 when he took up the role in the Diocese of Killaloe.
The new archbishop was born in Cork in 1952 and has worked in Liberia and Nigeria.
Head of the Irish Catholic Bishops' Conference, Archbishop Eamon Martin, welcomed the appointment.
He said: "I have known Archbishop Kieran since he became Bishop of Killaloe in 2010.
"In that time, like the people of Killaloe, I have come to know the warmth of his personality and his gentleness and pastoral sensitivity.
"As a new bishop myself, I have appreciated his wise counsel on many matters.
"Archbishop Kieran brings a perspective to the table of the Irish Episcopal Conference which is drawn from his wide experience of mission in Liberia and Nigeria."