The 115 cardinal-electors were locked in the chapel after swearing an oath of secrecy.
They will vote four times daily until two-thirds can agree on a candidate.
The election was prompted by the surprise abdication of Benedict XVI. There is no clear frontrunner to take over from him as head of the Roman Catholic Church.
The 85-year-old Benedict stepped down last month, saying he was no longer strong enough to lead the Church, which is beset by problems ranging from a worldwide scandal over child sex abuse to allegations of corruption at the Vatican Bank.
His resignation and the recent damage to the Church’s reputation make the choice of the cardinal-electors especially hard to predict.
They will weigh pressure for a powerful manager to reform the Vatican against calls for a new pope able to inspire the faithful, our correspondent adds.
At 16:30 local time on Tuesday, 115 cardinal-electors – all under 80, as those over 80 are excluded – entered the Sistine Chapel for the secret conclave to select Benedict’s successor, chanting the traditional Litany of the Saints.
Each man in turn stepped up and placed his hands on the Gospel to swear an oath in Latin.
Afterwards Msgr Guido Marini, papal master of ceremonies, called out the words “Extra omnes” – “Everybody out” – and the chapel doors were locked to outsiders.
From now on the cardinals will eat, vote and sleep in closed-off areas until a new pope is chosen.
Jamming devices in the Sistine Chapel should block all electronic communication and anyone tweeting would in any case risk being excommunicated.
Cardinals were now expected listen to a meditation by elderly Maltese Cardinal Prosper Grech before holding a first vote, after which their ballot papers will be burned.
The smoke that will drift out of the chapel’s chimney early in the evening is likely to be black – meaning no Pope has been elected.
From Wednesday, two votes will be held each morning and afternoon – with ballots burned after each session – until one candidate attains a two-thirds majority (77 votes).
Then the smoke will be white, meaning the 266th bishop of Rome will have been chosen.
Earlier on Tuesday the cardinals attended a “Mass for the Election of the Supreme Pontiff” in St Peter’s Basilica.
In his homily, the Dean of the College of Cardinals, Cardinal Angelo Sodano, praised the “brilliant pontificate” of Pope Benedict and implored God to grant another “Good Shepherd” to lead the church.
He outlined the mission Catholics believe was given by Jesus Christ to St Peter – the first Pope – emphasizing love and sacrifice, evangelization and the unity of the church.
The speech was more measured in tone than the address given in 2005 by Cardinal Joseph Ratzinger before he became Pope Benedict, which featured a fiery attack on the “dictatorship of relativism”.
On Tuesday morning several cardinals took to Twitter to say goodbye to their followers before being cut off from the outside world.
“Last tweet before the conclave: May Our Father hear and answer with love and mercy all prayers and sacrifices offered for a fruitful outcome,” South African Cardinal Wilfrid Napier tweeted.
Benedict – now known as Pope emeritus – resigned on 28 February after eight years in office, citing ill health. He was the first Pope in six centuries to do so.
As Cardinal Joseph Ratzinger in 2005, he was the marked favorite ahead of the conclave and was elected pope after just four rounds of voting.
The vote for his successor is expected to take much longer.
After 10 general congregations open to all cardinals, regardless of age – at which 160 cardinals spoke of the issues facing the Church and the qualities needed by its next leader – no clear frontrunner has emerged.
“Last time around there was a man of stature, three or four times that of any other cardinal,” French Cardinal Philippe Barbarin told reporters.
“That is not the case this time around. Therefore, the choice has to be made among one, two, three, four… a dozen candidates.
“We still don’t really know anything. We will have to wait for the results of the first ballot.”
New York Archbishop Cardinal Timothy Dolan told his priests there was hope that a new Pope could be chosen by Thursday.
Candidates named as contenders include Cardinal Angelo Scola of Milan, Brazil’s Odilo Scherer, and Cardinal Dolan himself – though he told one interviewer anyone who thought he was in with a chance might be “smoking marijuana”.
Conclave in numbers
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