He has chosen the name Pope Francis.
After announcing "Habemus Papum" - "We have a Pope" - a cardinal standing on the balcony of St Peter's Basilica revealed the identity of the new pontiff, using his Latin name.
Bergoglio had reportedly finished second in the 2005 conclave that produced Pope Benedict XVI, who last month became the first pope to resign in 600 years.
The 76-year-old archbishop of Buenos Aires has spent nearly his entire career at home in Argentina.
He thanked pope emeritus Benedict for his work for the church, and said the world should set off on a path of love and fraternity.
He delivered his first blessing to the huge crowd in St Peter's Square, asking for the prayers of "all men and women of good will" to help him lead the Catholic Church.
Francis becomes the 266th pontiff in the Church's 2,000-year history at a time of great crisis and difficulty.
Although a conservative, he is seen as a reformer and was not among the small group of frontrunners identified before the election.
He is the oldest of most of the possible candidates and is the first Jesuit to become pope.