The miracle involved the healing of a Brazilian man with several brain tumours in 2008, the Vatican said.
Mother Teresa died in 1997 and was beatified - the first step towards sainthood - in 2003.
She won the Nobel Peace Prize for her work with the poor in the slums of Indian city of Kolkata (Calcutta).
"The Holy Father has authorised the Congregation for the Causes of Saints to proclaim the decree concerning the miracle attributed to the intercession of blessed Mother Teresa," the Vatican said on Friday.
She is expected to be canonised in Rome in September.
Beatification by the Catholic Church requires one miracle, while the process of becoming recognised as a saint requires proof of at least two miracles.
Mother Teresa was beatified in 2003 after Pope John Paul II accepted as authentic a miracle attributed to her.
He judged that the curing of an Indian woman suffering from an abdominal tumour was the result of the supernatural intervention of the late Mother Teresa - a claim challenged by Indian rationalists.
There are few details about the recovery of the Brazilian man, whose life the Vatican says was saved in the second miracle.
His identity has not been disclosed to maintain the discretion needed for the investigation, the Catholic New Agency has said.
It says he was unexpectedly cured from brain tumours in 2008 after his priest prayed for Mother Teresa's intervention with God.
Born Agnes Gonxhe Bojaxhiu in Skopje, Macedonia, in 1910, she founded the Missionaries of Charity in 1949, dedicating her life to caring for impoverished and sick people in Kolkata.
Known as the "saint of the gutter", she earned worldwide acclaim for her efforts.
Her critics, however, accused her of mixing with dictators and peddling a hardline Catholicism.
Pope Francis has recognised a second miracle attributed to Mother Teresa, clearing the way for the Roman Catholic nun to be made a saint next year.