Tuesday was the feast of St. Joseph, and Francis made special mention in his homily of the carpenter saint's "lowly, concrete and faithful service."
He later telephoned Benedict, the former Joseph Ratzinger, to wish him a happy name day, and the Vatican said in a statement that the pope emeritus has been following the celebrations with "intense interest" and "assures his successor his continued closeness in prayer."
At the start of the Mass, Francis received the gold-plated fisherman's ring, which recalls how St. Peter fished for food and later for souls, and a wool stole symbolizing his role as shepherd of his flock. The ring was something of a hand-me-down, first offered to Pope Paul VI, who presided over the latter half of the Second Vatican Council, the meetings that brought the church into the modern world.
Francis also received vows of obedience from a half-dozen cardinals -- a potent symbol given that Benedict is still alive and was reportedly watching the proceedings on TV.
A cardinal intoned the rite of inauguration, saying: "The Good Shepherd charged Peter to feed his lambs and his sheep; today you succeed him as the bishop of this church."
Flags from around the world, including Argentina's blue and white flag, fluttered above the crowd, which the Vatican said numbered 150,000-200,000 people. Civil protection crews closed the main streets leading to the square to traffic and set up barricades for nearly a mile along the route to try to control the masses and allow official delegations through.
Some 132 official delegations attended, including more than a half-dozen heads of state from Latin America, a sign of the significance of the election for the region.
Francis's determination that his pontificate would be focused on the poor has resonance in a poverty-stricken region that counts 40 percent of the world's Catholics.
In the VIP section was U.S. Vice President Joe Biden, German Chancellor Angela Merkel, Argentine President Cristina Fernandez, Taiwanese President Ying-Jeou Ma, Zimbabwe President Robert Mugabe, Prince Albert of Monaco and Bahrain Prince Sheik Abdullah bin Haman bin Isa Alkhalifa, among others. All told, six sovereign rulers, 31 heads of state, three princes and 11 heads of government attended, the Vatican said.
Francis directed his homily to them, saying: "We must not be afraid of goodness or even tenderness."
After the Mass, Francis stood in a receiving line for nearly two hours to greet each of the government delegations in St. Peter's Basilica, chatting warmly and animatedly with each one, kissing the few youngsters who came along with their parents and occasionally blessing a rosary given to him.
Unlike his predecessors, he did so in just his white cassock, not the red cape.
Among the religious VIPs attending was the spiritual leader of the world's Orthodox Christians, Bartholomew I, who became the first patriarch from the Istanbul-based church to attend a papal investiture since the two branches of Christianity split nearly 1,000 years ago. Also attending for the first time was the chief rabbi of Rome.
Their presence underscores the broad hopes for ecumenical and interfaith dialogue in this new papacy, given Francis' own work for improved relations.
In a gesture to Christians in the East, the pope prayed with Eastern rite Catholic patriarchs and archbishops before the tomb of St. Peter at the start of the Mass, and the Gospel was chanted in Greek rather than the traditional Latin.
But it is Francis' history of living with the poor and working for them while archbishop of Buenos Aires that seems to resonate with ordinary Catholics who say they are hopeful that Francis can inspire a new generation of faithful who have fallen away from the church.
"As an Argentine, he was our cardinal. It's a great joy for us," said Edoardo Fernandez Mendia, an Argentine who was in the crowd. "I would have never imagined that it was going to be him."
Recalling another great moment in Argentine history, when soccer great Diego Maradona scored an improbable goal in the 1986 World Cup, he said: "And for the second time, the Hand of God came to Argentina."