The inauguration Mass for Pope Francis is under way in St Peter's Square in Rome, marking the official start of his papacy.
Francis earlier toured the square in an open-topped vehicle, descending to bless pilgrims behind the barriers.
Up to a million people, along with global political and religious leaders, are attending the Mass.
Francis was elected by a conclave of cardinals last week to take over from Benedict XVI.
Benedict became the first pontiff in 600 years to abdicate last month. Citing his age, 85, he said he could no longer continue in the post.
The first pontiff from the Americas, Francis has suggested he will take a more modest approach than predecessors.Papal ring
Pope Francis left his temporary residence at Casa Santa Marta shortly before 09:00 (08:00 GMT) and began touring St Peter's Square.
He waved to the hundreds of thousands of pilgrims, who flew flags and shouted: "Long live the Pope!"
Francis then entered St Peter's Basilica and donned his vestments.
One of the Pope's first duties was to go down to the tomb of St Peter to venerate it.
Francis was then presented with his papal pallium made of lambs' wool - symbolising his role as shepherd of his flock - in the main square.
He also received the "fisherman's ring" bearing the image of St Peter holding two keys. The ring is second hand and is made of silver-plated gold, not the solid gold worn by Francis' predecessor.
The Pope then received the obedience of the cardinals, and the Mass formally began.
It is being co-celebrated by around 180 clergymen, including Adolfo Nicolas, the superior general of Pope Francis' Jesuit order.
The list of attendees for Monday's Mass includes US Vice-President Joe Biden and the spiritual head of the Orthodox Church, Patriarch Bartholomew.
He will be the first Orthodox patriarch to attend a papal inauguration Mass since the two branches of Christianity split more than 1,000 years ago.
Thirty-three groups of guests from various Christian Churches are expected in total, according to the Vatican, along with 16 delegations from Jewish communities, as well as representatives of other faiths.
Communion will be distributed by 500 priests throughout the crowd.
The BBC's James Robbins, in Rome, says the ceremony will certainly be magnificent but perhaps more modest than in the past, with the Pope's profile more that of a global parish priest than a papal monarch.
The homily will be in Italian, but our correspondent says the Vatican has warned Pope Francis is likely to stray from his prepared text to stress his manifesto of seeking forgiveness and focusing on help for the poor.Argentine vigils
Before his election last week, Pope Francis was Cardinal Jorge Mario Bergoglio of Buenos Aires, and Argentine President Cristina Fernandez de Kirchner will attend the Mass.
On Monday, Ms Fernandez became the first foreign head of state to be received by Pope Francis and said she had asked for his intervention in the Falklands dispute between her country and the UK.
Hundreds of people gathered on Tuesday in Plaza de Mayor, the main square in Buenos Aires, to watch the Mass broadcast on giant screens set up outside the cathedral.
Correspondents say that in his first few days in office, Pope Francis has been striking an informal and spontaneous tone, preferring anecdotes and off-the-cuff remarks to scripted speeches.
Speaking on Saturday, he emphasised that he wanted "a poor Church, for the poor".
He is the first pontiff to take the name of Francis, choosing it to honour St Francis of Assisi, the 13th-Century son of an aristocrat who spurned a life of luxury to live with and for the poor.
Pope Francis said the Holy Spirit had inspired the resignation of Benedict XVI and guided the cardinals choosing him as the next pontiff.
At the end of a Mass he celebrated on Sunday, he waited outside the church and greeted people as they left, like a parish priest, asking many of them to "pray for me".
Later, just a few minutes after delivering the Angelus prayer, Pope Francis sent his first Tweet as pontiff, writing: "Dear friends, I thank you from my heart and I ask you to continue to pray for me. Pope Francis."