Mother Teresa has been declared a saint by Pope Francis in a ceremony at the Vatican.
Tens of thousands of pilgrims had arrived at the St Peter’s Square for the Mass and canonization.
Two miraculous cures of the sick after Mother Teresa’s death in 1997 have been attributed to her intercession.
In 2002, the Vatican ruled that an Indian woman’s stomach tumor had been miraculously cured after prayers to Mother Teresa.
Pope Francis cleared the way for sainthood last year when he recognized a second miracle attributed to Mother Teresa.
Meanwhile in India, a special Mass was celebrated at the Missionaries of Charity, the order Mother Teresa founded in Kolkata (Calcutta).
Many pilgrims arrived at the Vatican before dawn on September 4 to get a good spot among the masses for the ceremony.
Cardinal Angelo Amato read a brief biography of the nun’s work, then asked the Pope to canonize her in the name of the Church.
The pontiff responded: “After due deliberation and frequent prayer for divine assistance, and having sought the counsel of many of our brother bishops, we declare and define Blessed Teresa of Calcutta to be a saint and we enroll her among the saints, decreeing that she is to be venerated as such by the whole Church.”
Hundreds of Missionaries of Charity sisters attended the event, along with 13 heads of state or government.
Some 1,500 homeless people across Italy were also brought to Rome in buses to be given seats of honor at the celebration – and then a pizza lunch served by 250 nuns and priests of the Sisters of Charity order.
Large TV screens were set up at Mother House in Kolkata for the Vatican ceremony.
Nobel Peace Prize winner Mother Teresa founded a sisterhood that runs 19 homes.
She died in 1997 at the age of 87 and was beatified in 2003, the first step to sainthood.
Her work complements Francis’ vision of a Church that serves the underprivileged.
Mother Teresa’s canonization is a centerpiece of his Jubilee Year of Mercy.