He also offered a prayer to his predecessor, Pope Benedict, who resigned unexpectedly last month, after saying he was too frail to tackle the many problems assailing the world's largest organisation, which has an estimated 1.2 billion members.
"Good night and have a good rest," Bergoglio said before disappearing back into the opulent surroundings of the Vatican City - a far cry from his simple apartment in Buenos Aires.
Delighted priests, nuns and pilgrims danced around the obelisk in the middle of St. Peter's Square, chanting: "Long Live the Pope" and "Argentina, Argentina".
In his native Argentina, jubilant Catholics poured into their local churches to celebrate.
"I hope he changes all the luxury that exists in the Vatican, that he steers the Church in a more humble direction, something closer to the gospel," said Jorge Andres Lobato, a 73-year-old retired state prosecutor.
The 266th pontiff in the Church's 2,000-year history, Francis is taking the helm at a time of great crisis, with morale among the faithful hit by a widespread child sex abuse scandal and infighting in the Vatican bureaucracy.
His unexpected election answered some fundamental questions about the direction of the Church in the coming years.
After more than a millennium of European leadership, the cardinal-electors looked to Latin America, where 42 percent of the world's Catholics live. The continent is more focused on poverty and the rise of evangelical churches than questions of materialism and sexual abuse, which dominate in the West.
They also chose a man with long pastoral experience, rather than an academic and Vatican insider like Benedict.
"It seems that this pope will be more aware of what life is all about," Italian theologian Massimo Faggioli told Reuters.
Bergoglio was born into a family of seven, his father an Italian immigrant railway worker and his mother a housewife. He became a priest at 32, nearly a decade after losing a lung due to respiratory illness and quitting his chemistry studies.