Teresa's canonisation mass was attended by more than 100,000 pilgrims, including heads of state.
Pope Francis on Sunday proclaimed Mother Teresa a saint and hailed the revered Catholic nun as an embodiment of maternal love who talked truth to power on behalf of the poor.
"We may have some difficulty in calling her 'Saint' Teresa," the pontiff said. "Her holiness is so near to us, so tender and so fruitful that we continue to spontaneously call her Mother."
He added: "She made her voice heard before the powers of this world, so that they might recognise their guilt for the crime -– the crimes! -– of poverty they created."
Teresa's canonisation mass was attended by more than 100,000 pilgrims, including heads of state and hundreds of sari-clad nuns from her order, the Missionaries of Charity.
Queen Sofia of Spain and around 1,500 homeless people also looked on as Francis described Teresa's work in the slums of Kolkata as "eloquent witness to God's closeness to the poorest of the poor".
To applause, he added: "Mother Teresa loved to say, 'perhaps I don't speak their language but I can smile'. Let us carry her smile in our hearts."
Candles and flowers were laid on Teresa's tomb at the headquarters of her order in the Indian metropolis she is so closely associated with.
Lighting a candle, Konica Cecilia said Teresa had given her impoverished parents money to help them send her to school.
"I was fortunate to meet Mother. She was a living saint and an inspiration to me," the 32-year-old said. "My memories of her comfort me when I am in trouble."
Francis also used his sermon to recall Teresa's fervent opposition to abortion, which she termed "murder by the mother" in a controversial Nobel Peace prize speech in 1979.
She "ceaselessly proclaimed that the unborn are the weakest", he said.
Pizza lunch at Vatican
With the 16th century basilica of St Peter's glinting in the late summer sun, Francis led a ritual mass that has barely changed for centuries.
Speaking in Latin, he declared "blessed Teresa of Calcutta (Kolkata) to be a Saint... decreeing that she is to be venerated as such by the whole Church."
After the mass, the 79-year-old pontiff boarded an open-topped jeep and toured around St Peter's square and surrounding streets to a rapturous reception from tens of thousands of well-wishers.
Solangel Rojas had come from Cali in Colombia. Clutching a picture of Teresa to her heart, she said: "It is wonderful that she has been canonised. She was an example to us all."
Among those in the front rows at the mass were 1,500 people from shelters run by the Italian branches of Teresa's order. Later they were Francis's guests for a giant pizza lunch served by nuns and priests.
Teresa spent all her adult life in India, first teaching, then tending to the dying poor for decades before her death in 1997.
It was in the latter role, at the head of her now worldwide order, that Teresa became one of the most famous women on the planet.
Born to Kosovan Albanian parents in Skopje -- then part of the Ottoman empire, now the capital of Macedonia -- she won the 1979 Nobel Peace Prize and was revered around the world as a beacon for the Christian values of self-sacrifice and charity.
But she was also regarded with scorn by secular critics who accused her of being more concerned with evangelism than with improving the lot of the poor.
The debate over Teresa's legacy has continued after her death, with researchers uncovering financial irregularities in the running of her order and evidence mounting of patient neglect, insalubrious conditions and questionable conversions of the vulnerable in her missions.
By historical standards, Teresa has been fast-tracked to sainthood. John Paul II was a personal friend and as the pope at the time of her death, he was responsible for her being beatified in 2003.
Achieving sainthood requires the Vatican to approve accounts of two miracles occurring as a result of prayers for Teresa's intercession.
The first one, ratified in 2002, was of an Indian woman, Monica Besra, who says she recovered from ovarian cancer a year after Teresa's death -- something local health officials have put down to medicine rather than prayer.
In the second, approved last year, Brazilian Marcilio Haddad Andrino says his wife's prayers to Teresa led to brain tumours disappearing. Eight years later, Andrino and his wife Fernanda were in the congregation on Sunday.
Also presented was London-based Indian expatriate Abraham. "She practised Christianity," he said. "The majority of Christians only spend their time talking about it."