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.
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!”
Rodrigo Grajales, a 31-year-old Colombian priest, told Agence France-Presse: “With Pope Francis, the Church will be closer to the people and to the modern world.”
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.
With the reception of the pallium and ring, Francis officially began his office as the 266th pope.
The Pope then received the obedience of the cardinals, and the Mass formally began.
Francis is now delivering his homily, in Italian.
The Mass 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.