Pope Francis first 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.
Pope Francis was elected by a conclave of cardinals last week to take over from Benedict XVI.
Pope Benedict XVI 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, formerly Argentine Cardinal Jorge Mario Bergoglio, left his temporary residence at Casa Santa Marta shortly before 09:00 and began touring St Peter’s Square.
The pontiff waved to the hundreds of thousands of pilgrims, who flew flags and shouted: “Long live the Pope!”
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.
Pope Francis was then presented with his papal pallium made of lambs’ wool – symbolizing 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.
Pope Francis then delivered his homily, in Italian.
It began by focusing on Joseph and his role as protector – of Mary, Jesus and the Church.
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