The 76-year-old from Buenos Aires is the first Latin American and the first Jesuit to be pontiff. An hour earlier, white smoke from the Sistine Chapel chimney announced the new Pope's election. He will be installed officially in an inauguration Mass on Tuesday 19 March, the Vatican said. Pope Francis replaces Benedict XVI, who resigned last month at the age of 85, saying he was not strong enough to lead the Church.
He has telephoned Benedict and is planning to meet him, a Vatican spokesman said. Pope Francis takes the helm at a difficult time for the Catholic Church, facing an array of challenges which include the role of women, interfaith tensions and dwindling congregations in some parts of the world.
"Viva il papa!" they chanted, as they waited to learn his name. Once the crowd had been told, the chants quickly turned to: "Fran-ces-co! Fran-ces-co!" And then, to trumpet fanfare, the balcony curtains parted and the new Pope appeared above them, to bless them - but only after he had asked them to pray with him, and for him. The people were touched, and roared their approval.
"Habemus Papam Franciscum," was the first tweet by the papal account @pontifex since Benedict stood down last month. The election was met with thunderous applause at the cathedral in Buenos Aires, Pope Francis' home city.
Throughout Latin America - home to 40% of the world's 1.2 billion Catholics - people reacted with delight and surprise. "It's a huge gift for all of Latin America. We waited 20 centuries. It was worth the wait," said Jose Antonio Cruz, a Franciscan friar in the Puerto Rican capital San Juan, quoted by the Associated Press.
"Everyone from Canada down to Patagonia is going to feel blessed. This is an event."
US President Barack Obama sent "warm wishes" on behalf of the American people to the newly elected pontiff, hailing the Argentine as "the first pope from the Americas."
- Born Jorge Mario Bergoglio on 17 December 1936 (age 76) in Buenos Aires, of Italian descent
- Ordained as a Jesuit in 1969
- Studied in Argentina and Germany
- Became Cardinal of Buenos Aires in 1998
- Seen as orthodox on sexual matters but strong on social justice
Argentina's President Christina Fernandez de Kirchner wished him a "fruitful pastoral mission". She is expected to attend the Pope's inauguration Mass on Tuesday, as is US Vice President Joe Biden, himself a Catholic.
United Nations Secretary General Ban Ki-moon said he looked forward to cooperation under Pope Francis's "wise leadership. Correspondents say Cardinal Bergoglio was a surprise choice and not among a small group of frontrunners before the election. Many observers were also expecting a younger pope to be elected. He is regarded as a doctrinal conservative but seen as a potential force for reform of the Vatican bureaucracy, which may have won the support of reforming cardinals. However, he is known more than anything for his humility. He has spent almost his entire career in Argentina and often travels to work by bus.
The BBC's Marcia Carmo in Buenos Aires says Cardinal Bergoglio's sermons always had an impact in Argentina: he often stressed social inclusion and indirectly criticised governments that did not pay attention to those on the margins of society.
The name he has taken is reminiscent of St Francis of Assisi, the 13th Century Italian reformer and patron saint of animals, who lived in poverty. The saint was said to have been summoned by God to repair a Church in ruins. Cardinal Bergoglio, whose family roots are Italian, is generally thought to have come second in the last conclave in 2005, which elected Benedict XVI as Pope. The 115 cardinals involved in the 2013 election were in isolation since Tuesday afternoon, and held four inconclusive votes.
At least 77 of them, or two-thirds, would have had to vote for a single candidate for him to be elected Pope.
Before the conclave began, there appeared to be no clear choice to replace Benedict.