"For the honour of the Blessed Trinity... we declare and define Blessed Teresa of Calcutta (Kolkata) to be a Saint and we enrol her among the Saints, decreeing that she is to be venerated as such by the whole Church," the pontiff said in Latin.
Francis said that even though the nun had been declared a saint, she would always be Mother Teresa to the Catholic family.
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 and give it to those whom we meet along our journey, especially those who suffer."
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. The ceremony came a day before the 19th anniversary of Teresa's death in Kolkata where Teresa spent nearly four decades working in wretched slums.
With the 16th century basilica of St Peter's and an azure sky providing the backdrop, the faithful basked in the late summer sun as Francis presided over a ritual mass that has barely changed for centuries. Such was the demand from pilgrims, the Vatican could easily have issued double the number of tickets but for space and security restrictions.
Helicopters had buzzed overhead earlier, testifying to a huge security operation. Some 3,000 officers were on duty to ensure the day passed off peacefully for the pilgrims and scores of dignitaries from around the world.
Among the crowd were some 1,500 people who are helped by the Italian branches of Teresa's order, the Missionaries of Charity.
After the mass they were to be Francis's guests at the Vatican for a giant pizza lunch served by 250 sisters and 50 male members of the order.
Teresa spent all her adult life in India, first teaching, then tending to the dying poor.
It was in the latter role, at the head of her now world-wide 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.