Pope Francis has declared Mother Teresa a saint, honouring the nun who cared for the world's most destitute.
Applause erupted around St Peter's Square even before Francis finished pronouncing the rite of canonisation at the start of the Mass at the Vatican.
For Francis, Mother Teresa put into action his ideal of the church as a merciful "field hospital" for the poorest of the poor, those suffering both material and spiritual poverty.
Hundreds of Missionaries of Charity sisters in their trademark blue-trimmed saris had front-row seats at the Mass alongside 1,500 homeless people and 13 heads of state or government, including Queen Sofia of Spain.
Francis praised Mother Teresa as the merciful saint who defended the lives of the unborn, sick and abandoned - and who shamed world leaders for the "crimes of poverty they themselves created".
Francis held St Teresa up as a model for today's Christians during his homily for the nun.
Speaking from the steps of St Peter's Basilica, he said she spent her life "bowing down before those who were spent, left to die on the side of the road, seeing in them their God-given dignity".
He added: "She made her voice heard before the powers of the world, so that they might recognise their guilt for the crimes of poverty they themselves created."
As if to emphasise the point, Francis repeated the line "the crimes of poverty they themselves created".
Thousands of other pilgrims gathered at St Peter's Square for the ceremony.
Throughout the night, they prayed at vigils in local churches and flocked before dawn to the Vatican under heavy security to try to get a good spot for the Mass that was expected to draw more than 100,000 people.
"I think most of all we are thankful to her (Mother Teresa) for the message, for really changing our lives with her example, humility, being close to the poorest of the poor," said Simone Massara as he prayed with his wife at a vigil at the Basilica of Sant'Andrea della Valle before the Mass.
While Francis was clearly keen to hold Mother Teresa up as a model for her joyful dedication to the poor, he was also recognising holiness in a nun who lived most of her adult life in spiritual agony sensing that God had abandoned her.
According to correspondence that came to light after she died in 1997, Mother Teresa experienced what the church calls a "dark night of the soul" - a period of spiritual doubt, despair and loneliness. In Mother Teresa's case, it lasted for nearly 50 years - an almost unheard of trial.
For the Rev Brian Kolodiejchuk, the Canadian priest who spearheaded Mother Teresa's saint-making campaign, the revelations were further confirmation of her heroic saintliness.
He said that by canonising her, Francis is recognising that Mother Teresa not only shared the material poverty of the poor but the spiritual poverty of those who feel "unloved, unwanted, uncared for".
"What she described as the greatest poverty in the world today (of feeling unloved) she herself was living in relationship with Jesus," he said in an interview on the eve of the canonisation.
Born on August 26 1910 to Albanian parents in Skopje, Mother Teresa came to India in 1929 as a sister of the Loreto order. In 1946, she received what she described as a "call within a call" to found a new order dedicated to caring for the most unloved and unwanted, the "poorest of the poor".
In 1950 she founded the Missionaries of Charity, which went on to become a global order of nuns - identified by their trademark blue-trimmed saris, as well as priests, brothers and lay co-workers.
She was awarded the Nobel Peace Prize in 1979.
She died in 1997 after a lifetime spent caring for hundreds of thousands of destitute and homeless poor in Kolkata, for which she came to be called the "saint of the gutters".
St John Paul II, her most ardent supporter, fast-tracked her for sainthood and beatified her before a crowd of 300,000 in 2003.
Pope Francis is following in the footsteps of Mother Teresa by offering some 1,500 homeless people a pizza lunch at the Vatican after her canonisation Mass.
The homeless came to Rome overnight on buses from across Italy to take part in the Mass. They got seats of honour for the celebration.
A Neapolitan pizza maker brought 20 people and three pizza ovens to cook the lunch, which will be served to the guests by some 250 sisters and priests.