The 76-year-old Argentine was elected by 115 cardinals on the second day of their conclave in the Sistine Chapel, in Vatican City.
Bergoglio is the first pope ever from the Americas. Bergoglio has chosen the name Francis, another first.
French cardinal Jean-Louis Tauran made the announcement in Latin from the balcony of St. Peter's Basilica in the early evening on March 13 more than an hour after white smoke billowed from the makeshift chimney on the Sistine Chapel, signaling a new pope had been chosen.
"I announce to you a great joy, we have a pope. His name is Jorge Mario Bergoglio and he has taken the name Francis."
A bit later, Pope Francis addressed the tens of thousands of flag-waving pilgrims in Italian.
"Brothers and sisters, good evening. As you know the duty of the conclave is to give Rome a bishop. It seems that my brother cardinals went almost to the end of the world. But we are here."
The son of an Italian immigrant, Bergoglio replaces retired Pope Benedict XVI, who last month became the first pope to resign in 600 years.
Francis praised his predecessor.
"First of all I would like to pray for Benedict, our bishop emeritus. We pray altogether for him for God to bless him and for the Madonna to hold him."
Bergoglio reportedly finished second in the 2005 conclave that selected Benedict.
But this time around, analysts say, Bergoglio, was not considered a front-runner.
"I think it was a surprise on the immediate level. When the name of the pope was first spoken in Latin I think those of us who were familiar with the cardinals who were the front runners started to think, ’Was there a Jorge amongst them, and who would it have been?’ And then when the official announcement came, I think many of us thought, ‘Wait a minute, who is that?’" Yale University Divinity School Professor of Liturgical Studies Teresa Berger told RFE/RL.
Berger said his selection had great significance.
"It’s huge. I had already hoped for a Latin American pope in the previous conclave. This is a wonderful recognition of the weight of the Church’s numbers, in a sense – moving elsewhere than the European traditional heartland of the Church," Berger said.
World political and spiritual leaders have been reacting to the news.
U.S. President Barack Obama applauded the selection of the first pope from the Americas as a sign of the region's strength and vitality.
Calling the task of leading the modern Catholic Church "sacred work," Obama said he looked forward to working with the new pope to promote peace, security, and dignity for people of all faiths.
UN Secretary-General Ban Ki-moon said he hoped Francis would continue to promote interfaith dialogue.
The Russian Orthodox Church welcomed the election and hoped "that relations between the Orthodox and Catholic churches will develop in a positive spirit."
German Chancellor Angela Merkel said she was "especially happy for the Christians of Latin America."
Francis faces many challenges including sex scandals and falling membership, mainly in Europe.