It will take several days before there is an installation Mass, because it will take time for world leaders to arrive, Lombardi had said.
[Updated at 4:45 p.m. ET]
U.S. President Barack Obama has weighed in.
Obama offered his prayers and "warm wishes" Wednesday to newly elected Pope Francis. Obama called him "a champion of the poor and the most vulnerable among us," and also said his election as "the first pope from the Americas ... speaks to the strength and vitality of (that) region."
[Updated at 4:44 p.m. ET]
The pope's election has caught the attention of the Internet crowd, to put it lightly. Facebook says that its users' top terms about 70 minutes ago were:
1) Pope; 2) Jorge Bergoglio; 3) Vatican; 4) White smoke; 5) Cardinal; 6) Catholic; 7) Decision; and 8) Papal.
[Updated at 4:31 p.m. ET]
Latin Americans in St. Peter's Square are thrilled.
"As a youth, and as a Catholic student, and as a Mexican, I am absolutely overwhelmed with emotion (at) the fact that we have a new pope that will represent that part of the (world)," a woman from Ciudad Juarez, Mexico, told CNN. "That is something very exciting. I feel that Mexico has been a country that has suffered a lot, and so has Latin America, but it is a people that has always put trust in God, so it is absolutely wonderful to represent our part of the world this time around."
Beside her, a woman from Mexico City said her heart jumped when she heard the announcement that a pope had been picked.
"I'm so excited," she said. "It's a reason of being proud tonight, because Latin America is a very important Catholic area and now it's going to be totally represented here, so I'm so proud and I'm so happy today. ... It's going to help a lot, a Latin American pope, it's going to help. It's going to rebuild many things, and it's a new start."
[Updated at 4:22 p.m. ET]
Let's take a look at some reaction to Francis' election. Here's what Cardinal Timothy Dolan of New York -- by some accounts a pre-conclave contender for the papacy -- had to say, shortly after he participated in the conclave:
"Pope Francis I stands as the figure of unity for all Catholics wherever they reside," Dolan said in a statement released by the United States Conference of Catholic Bishops. "Intense prayer from all around the world surrounded the election of Pope Francis I. The bishops of the United States thank God for the guidance of the Holy Spirit and the inspired choice of the College of Cardinals."
And the Church of England, the country's official church denomination, offered a prayer Wednesday for the newly elected pope.
"Guide him by by your spirit, give him grace to lead people in prayer and zeal, and to follow in the footsteps of Jesus Christ, your son our Lord," the prayer read.
[Updated at 4:08 p.m. ET]
CNN Vatican expert John Allen has reported previously, for the National Catholic Reporter, that the new pope may have been the runner-up in the 2005 election that saw Cardinal Joseph Ratzinger become Benedict XVI. Allen noted that there's no official account of that election - it is officially secret, after all - but various reports had Bergoglio coming in second in 2005.
[Updated at 3:51 p.m. ET]
Choosing the name Francis is powerful and ground-breaking, CNN Vatican expert John Allen says.
As noted earlier, this is the first Pope Francis. Also, the name parallels one of the most venerated figures in the Roman Catholic Church, St. Francis of Assisi.
Allen described the name of Pope Francis as "the most stunning" choice and "precedent shattering."
"There are cornerstone figures in Catholicism" such as St. Francis, Allen said. Figures of such stature as St. Francis seem "irrepeatable -- that there can be only one Francis," Allen added.
[Updated at 3:48 p.m. ET]