Argentine Cardinal Jorge Mario Bergoglio has been elected the Catholic Church's Pope, taking the name Francis.
Appearing on a balcony over St Peter's Square in Rome, he asked the faithful to pray for him, with cheers erupting as he gave a blessing.
The 76-year-old from Buenos Aires is the first Latin American and the first Jesuit to be pontiff.
Messages of goodwill have poured in from around the world. The Pope's inaugural Mass will be next Tuesday.
Pope Francis replaces Benedict XVI, who resigned last month at the age of 85, saying he was not strong enough to lead the Church.
Francis has telephoned Benedict and is planning to meet him, a Vatican spokesman said.
The new Pope 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.
The election of a new Pope was signalled by white smoke from the Sistine Chapel chimney on Wednesday evening.
About an hour later, the name of the new Pope was read out.
The BBC's James Robbins, in St Peter's Square, says that at first the crowd was unsure who this man was, but they seemed to warm to his humour.
He began his address to the crowds by offering a prayer for his predecessor.
In a light-hearted moment, he said his fellow cardinals had gone to the "ends of the Earth" to find a bishop of Rome.
He went on to ask the crowd to "pray to God so that he can bless me", before calling on the world to set off on a path of love and fraternity.
"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".
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.
UK Prime Minister David Cameron said it was a "momentous day" for Catholics, while Archbishop of Canterbury Justin Welby, leader of the world's Anglicans, offered him "every blessing".
"I look forward to meeting Pope Francis, and to walking and working together to build on the consistent legacy of our predecessors," he said in a statement.
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.
"He is a very serious figure, with moral clout... but very down to earth," said Monsignor Eduardo Garcia of the Cathedral of Buenos Aires.
The name the new Pope 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.