Appearing on a balcony over the square, he asked the faithful to pray for him. Cheers erupted as he gave a blessing.
The first Latin American and the first Jesuit to be pontiff, he will call himself Francis I.
An hour earlier, white smoke from the Sistine Chapel chimney announced the new Pope’s election.
Cardinal Bergoglio replaces Benedict XVI, who resigned last month at the age of 85, saying he was not strong enough to lead the Church.
The 115 cardinals have been 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 was no clear frontrunner to replace Benedict.
Crowds with umbrellas massed in the square flying flags from around the world.
The Catholic News Agency said people were running through the streets of Rome, hoping to reach St Peter’s Square in time for the appearance of the new Pope.