"Brother and sisters, good evening," said Francis. "It seems the conclave went to the other side of the world to find a new pope."
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The crowd, with eyes fixed on the burgundy-draped balcony, chanted: "Viva il Papa!" or "Long live the pope!"
Francis asked the faithful to pray for his predecessor, who was reportedly watching the event on TV.
He then intoned the Lord's Prayer.
"Pray for me, I'll see you soon. Good night and rest well," he said.
Bergoglio is the first ever pontiff from the Americas and the first non-European pope in over 1,300 years.
He was born in Buenos Aires on Dec. 17, 1936. His father, an immigrant from Italy, was a railway worker. Bergoglio, one of five children, had early dreams of becoming a chemist, but eventually chose the path to priesthood when he entered the Society of Jesus in 1958.
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Barely mentioned in the speculation about the candidates for papacy, the soft-spoken Bergoglio is known as a humble man who refused the luxuries that previous Buenos Aires cardinals enjoyed.