The news, which was confirmed by the Vatican on Monday, has left Catholics across Ireland stunned.
Pope Benedict will become the first pope to resign in centuries when he steps down as head of the Catholic Church at the end of the month.
His resignation comes after almost eight years in the post, having been elected back in April 2005 at the age of 78 - the oldest person to take the office in nearly 300 years.
"The pope announced that he will leave his ministry at 8pm (7pm UK time) on 28 February," spokesman Federico Lombardi said.
Cardinal Seán Brady, the leader of Ireland's Catholics, said it was an "historic day".
Pope Benedict has resigned in circumstances of his own choosing. While it is a shock to me, we can be certain that Pope Benedict has made this decision after very careful and prayerful reflection.
Cardinal Seán Brady
Paying tribute, he added: "It hasn't happened in centuries but on reflection it's not that surprising, because I think he is the man who has the courage to take decisions like that and he has done so on careful reflection. It takes courage but it also comes from a love of the church."
Earlier, Pope Benedict announced his decision in Latin to a meeting of Vatican cardinals and explained that his failing health was the reason behind his resignation.
"In today's world, subject to so many rapid changes and shaken by questions of deep relevance for the life of faith, in order to govern the bark of St. Peter and proclaim the Gospel, both strength of mind and body are necessary," he said.
"Strengths which, in the last few months, have deteriorated in me to the extent that I have had to recognise my incapacity to adequately the ministry entrusted to me."
As the former Cardinal Joseph Ratzinger, he saw first-hand how the man he was to later replace - Pope John Paul II - suffered with debilitation towards the end of his papacy.
But Michael Kelly, editor of the Irish Catholic newspaper, told UTV the timing of Pope Benedict's announcement had caught many people off guard.
"There had been some talk two years ago that Pope Benedict might resign due to failing health, but that came and went with no sign of a resignation," he said.
"There has been no indication up until this - Pope Benedict had a full schedule of events over the weekend, he has a full schedule of events planned in the run up to Easter.
"I don't think anyone saw this coming."
After having repeatedly examined my conscience before God, I have come to the certainty that my strengths due to an advanced age are no longer suited to an adequate exercise of the Petrine ministry.
Pope Benedict XVI
Political leaders across Ireland have expressed shock at the news and paid tribute to Pope Benedict.
Northern Ireland's deputy First Minister, Martin McGuinness, said: "The announcement of Pope Benedict's resignation has taken everyone by surprise.
"Interest understandably centres on his health and the deteriorating nature of it. The resignation of a Pope is a most unusual occurrence and this clearly suggests that Pope Benedict's has such very serious concern about his health that he feels he must resign.
"The thoughts and prayers of everyone will be for Pope Benedict."
Taoiseach Enda Kenny said: "On behalf of the Government and people of Ireland, I would like to extend best wishes to His Holiness Pope Benedict XVI following his declaration today that he intends to step down from his office.
"This is clearly a decision which the Holy Father has taken following careful consideration and deep prayer and reflection. It reflects his profound sense of duty to the Church, and also his deep appreciation of the unique pressures of spiritual leadership in the modern world."
President Michael D Higgins said he has written to the pope expressing his good wishes on his decision to retire.
"In his letter, President Higgins acknowledged the scholarship and personal commitment that Pope Benedict brought to his leadership of the Roman Catholic community over the past eight years and wished him every peace and fulfillment in his retirement," the president's office said in a statement.
Last summer, speculation was rife that Pope Benedict would be making visits to both Northern Ireland and the Republic in the near future.
Such a visit would have been a first for Northern Ireland and only the second of its kind for the Republic.
The late Pope John Paul II visited Ireland in 1979, but plans to cross the border had to be scrapped amid an upsurge in violence.
Pope Benedict visited Britain in 2010, but again there was no stop in Northern Ireland.
As thoughts turn to finding a replacement for the pontiff, Michael Kelly said he didn't think it would be something that would have been given a lot of thought prior to Monday's announcement.
I think probably there might be a push for a younger pope.
"But a health warning with that is that the people who will choose the new pope, and most likely will be the new pope, are the members of the College of Cardinals - who are generally men in their 60s and 70s. So they're not very young and it will all be relative.
"The other side to that as well is, if you choose a pope who's very young, he may well want to be pope for 25, 30 years - like John Paul II. Whether or not the cardinals have an appetite for that, I think it's too soon to say.
"This is something they won't have had a great deal of discussion among themselves about because it is very unexpected."
Pope Benedict, 85, is the 265th pope - the papacy will remain vacant until a successor is elected.
Contenders include Cardinal Angelo Scola, archbishop of Milan; Cardinal Christoph Schoenborn, the archbishop of Vienna; and Cardinal Marc Ouellet, the Canadian head of the Vatican's office for bishops.
The last pope to resign was Pope Gregory XII, who stepped down in 1415 in a deal to end the Great Western Schism among competing papal claimants.
It is thought Pope Benedict will retire to spend his final years in the peace and quiet of his native Bavaria in Germany.
His 89-year-old brother, Georg Ratzinger, said that the resignation was simply part of a "natural process" as the pontiff had been having increasing difficulty walking and had been advised by his doctor not to undertake any more transatlantic travel.
"His age is weighing on him - at this age, my brother wants more rest," he said.