He led the Catholic Church for fewer than eight years until, in 2013, he became the first Pope to resign since Gregory XII in 1415.
Benedict spent his final years at the Mater Ecclesiae monastery within the walls of the Vatican where he passed away at 09:34 (08:34 GMT) on Saturday.
His successor Pope Francis will lead the funeral on 5 January.
The Vatican said the body of the Pope Emeritus will be placed in St Peter’s Basilica from 2 January for “the greeting of the faithful”.
Bells rang out from Munich cathedral and a single bell was heard ringing from St Peter’s Square in Rome after the former pope’s death was announced.
The head of the Catholic Church in England and Wales, Cardinal Vincent Nichols, said Pope Benedict was “one of the great theologians of the 20th century”.
In a statement he said: “I remember with particular affection the remarkable Papal Visit to these lands in 2010. We saw his courtesy, his gentleness, the perceptiveness of his mind and the openness of his welcome to everybody that he met.”
British Prime Minister Rishi Sunak called the former pope “a great theologian whose UK visit in 2010 was an historic moment for both Catholics and non-Catholics throughout our country”.
King Charles III said he received the news of Pope Benedict’s death “with deep sadness” and recalled “with fondness” meeting the him during a visit to the Vatican in 2009.
“I also recall his constant efforts to promote peace and goodwill to all people, and to strengthen the relationship between the global Anglican Communion and the Roman Catholic Church.”
French President Emmanuel Macron said Pope Benedict “worked with soul and intelligence for a more fraternal world” and said his thoughts went out to Catholics in France and around the world.
Italy’s Prime Minister Giorgia Meloni said Pope Benedict “was a giant of faith and reason”.
“He put his life at the service of the universal Church and spoke, and will continue to speak, to the hearts and minds of men with the spiritual, cultural and intellectual depth of his Magisterium.”
The German chancellor, Olaf Scholz, said for many, not only in Germany, Pope Benedict was “a formative figure of the Catholic Church, a forthright personality and a clever theologian”.
Irish President Michael D Higgins said the former pope will be remembered for “his untiring efforts to find a common path in promoting peace and goodwill throughout the world”.
Archbishop of Canterbury, Justin Welby, said Pope Benedict was “one of the greatest theologians of his age – committed to the faith of the Church and stalwart in its defence”.
Russian President Vladimir Putin praised Pope Benedict as a “defender of traditional Christian values,” in his New Year address to the nation.
Following news of the former pope’s death people began gathering in St Peter’s Square in Rome.
Annamaria, 65, and Patrizia, 64, visiting from the northern Italian city of Bologna, said they went there immediately as soon as they heard about the death.
“We came here to pray. He was a great pontiff, certainly very different from Francis, he was a great intellectual and scholar. Like the rest of the Church we will always remember him,” Annamaria told the BBC.
Barbara Bernadas, a tourist from the Spanish city of Barcelona, said she and her boyfriend felt a sense of bewilderment when they heard the news.
“We learned of his death just as we were in St Peter’s Square. A tourist guide was just telling us where Benedict lived, it feels surreal. What will happen now? This situation is unprecedented; there are no protocols to follow for what will happen now. Certainly it is an unprecedented historical moment,” she said.
Although the former pontiff had been ill for some time, Vatican authorities said there had been an aggravation in his condition because of advancing age.
On Wednesday, Pope Francis appealed to his final audience of the year at the Vatican to “pray a special prayer for Pope Emeritus Benedict”, whom he said was very ill.
Born Joseph Ratzinger in Germany, Benedict was 78 when in 2005 he became one of the oldest popes ever elected.
For much of his papacy, the Catholic Church faced allegations, legal claims and official reports into decades of child abuse by priests.
Earlier this year the former pope acknowledged that errors had been made in the handling of abuse cases while he was archbishop of Munich between 1977 and 1982.
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