Church reaction: The Archbishop of Armagh, Dr Seán Brady, called on Irish Catholics and "all people of good will" to pray for the new Pope.
He described Cardinal Ratzinger's election as "a source of great joy and hope for Catholics throughout the world and an important event for the whole human family.
"At the beginning of the third millennium we are blessed with a deeper sense of our common humanity and with a shared sense of responsibility in striving for a more just and peaceful world.
"Pope Benedict XVI will play a critical part in progressing this search, in engaging with people of all faiths, and none, in constructive dialogue about the joy and hopes, the challenges and the fears of the world. This is a daunting prospect."
The Archbishop of Dublin, Dr Diarmuid Martin, said: "I have had the privilege of knowing the new Pope on a personal level for many years, particularly during the years in which I resided at the Teutonic College in Vatican City, where Cardinal Ratzinger was a regular visitor.
"The new Pope is universally recognised as a man of extraordinary intellect, of deep spirituality and as one of the leading theologians of the late 20th century. His lifestyle is one of simplicity, indeed austerity."
Later in an RTÉ interview he was asked whether the new Pope, who had been a controversial figure, could act as a unifying force in the church. "I think he can," Dr Martin replied.
He said Cardinal Ratzinger had never courted popularity, and therefore had always been free to say what he believed was the message of the Gospel.
"The Pope is in a unique position to promote respect between those of other faiths, as did the late John Paul II.
"In a globalised world, the united voice of people of faith will be increasingly called upon against the evils of war and poverty. We pray that the new Pope Benedict XVI will be led by the Holy Spirit in the task to which he has been elected."
The Archbishop of Armagh and Primate of All Ireland, the Rev Dr Robin Eames, extended to Archbishop Seán Brady, the clergy and people of the Roman Catholic Church in Ireland the prayerful good wishes of the Church of Ireland on the election of Cardinal Ratzinger.
"I pray that God will bless and guide him as he takes up his new privileges and heavy responsibilities at this time," the archbishop said.
The Right Rev Peter F Barrett, Bishop of Cashel and Ossory and chairman of the Christian Unity Committee of the Church of Ireland, said "the announcement of the election of His Holiness Pope Benedict XVI is an historic occasion for the church.
"We extend to the new Pope our sincere and prayerful good wishes in the risen Lord at the commencement of his papacy.
"We extend also to our brothers and sisters in the Roman Catholic Church in Ireland, the assurance of our ongoing commitment to the ecumenical pilgrimage at home and on a wider scale.
"It is fitting that the new pontificate should begin in this Easter season of joy and gladness, as we continue to celebrate the resurrection of our Lord Jesus Christ, who 'makes all things new' and who, in the fellowship of the Holy Spirit, calls us to reflect together upon the mystery of His loving presence in the Church and in the world."