Monsignor Eamon Martin, the administrator of the diocese and who is in line to be the next leader of Catholics in Ireland, has hailed what he believes will be a new era brought about by Pope Francis.
The new pontiff, Argentinian former cardinal Jorge Mario Bergoglio, is the first pope to be selected from outside Europe in over a millennium and the first ever from the Americas.
Monsignor Martin asked: "Are we ready to hear the message that a non-European might bring to our western world - maybe waking us up to big issues that are out there in the world?"
I think he's going to shake us up.
Monsignor Eamon Martin
While Pope Francis is from Buenos Aires, he is actually of Italian descent and takes his name from one of Italy's patron saints - St Francis of Assisi, an Italian friar who founded the Franciscan Order.
Members of the Order are currently visiting schools in Derry and they also spoke to UTV about their great joy at the new pope's choice of name.
Friar Alessandro Brustenghi, who is from Assisi, said: "I am very excited because it is wonderful to have now a pope with the name of Francis."
Belfast based Jesuit priest Fr Alan McGuckian was hearing confession on Wednesday evening when a child showed him the results of the secret conclave vote on her iPhone.
He said the appointment of Cardinal Bergoglio came as "a complete shock."
"I actually didn't think a Jesuit would ever be elected Pope," he said, explaining that the order was established to be at the service of the church, and especially, to be at the service of the Pontiff.
"It was a clear understanding that no Jesuit would ever seek High office and that indeed he [the individual] would actually refuse it if he was offered it because our role was not to have those kind of offices. It was to serve - and particularly serve the Pope.
"So the idea that a Jesuit would be the Pope just seems unreal," he said, before adding that the appointment was a source of great pride for the Order.
Discussing Pope Francis, Fr McGuckian said that he was "obviously a complex and impressive man."
"He is clearly a very Orthodox Catholic - Orthodox doctrinally - but he is a radical man."
The choice of his Papal name speaks volumes, he added.
The Church of Ireland's Most Reverend Richard Clarke, Archbishop of Armagh and Primate of All Ireland, and Reverend Kenneth Lindsay, president of the Methodist Church, have already joined world leaders - including British Prime Minister David Cameron, Irish Taoiseach Enda Kenny and US President Barack Obama - in offering their welcome and prayers for the new pope.
On Thursday, Jorge Mario Bergoglio's first full day as Pope Francis, the pontiff started off with a visit to Rome's Basilica of Santa Maria Maggiore.
Just after his election the previous evening, he told the thousands in St Peter's Square that he would pray to the Madonna to watch over all of Rome.
And now, we take up this journey ... a journey of fraternity, of love, of trust among us.
But that only came after he'd been to the priests' residence where he'd been staying during the conclave, to pick up his belongings and pay his bill - in a nod to the humility for which he is known.
It is understood that Pope Francis will celebrate his inaugural mass in the Sistine Chapel later on Thursday, when he may outline his priorities.
In the coming days, he also intends to visit his predecessor Benedict XVI at Castel Gandolfo.
As the 266th pontiff, Pope Francis inherits a Catholic Church in need of leadership - with its members hoping for guidance to address falling numbers, internal divisions, and the ongoing fall-out from the clerical abuse scandal.