Tradition holds that October has been celebrated as the month of the rosary since 1571, and the victory of the Catholic League (an alliance of Spain, Venice, the Papal States, Genoa, Savoy, and Malta) over the forces of the Ottoman Empire who were seeking to take over Italy in an effort to move into the heart of Europe. It was October 7, 1571 when the battle was fought and the Catholic League was able to overcome the Ottoman forces.

Prior to the ships sailing off towards battle, Pope Pius V prayed the rosary, asking for Our Lady’s intercession in victory, and every man on board carried a rosary. For this reason, as soon as the men returned from the battle, the good pope declared a feast day for Our Lady of Victory. A rosary procession was offered in St. Peter’s square after the victory and in time the whole month became associated with the rosary, rather than just one day. Pope Leo XIII officially established October as the Month of the Rosary in the 1884. That year, he published Superiore Anno, an encyclical which was focused on recitation of the holy rosary. In it, he called for the entire Church to dedicate the whole of the month to the rosary and pray it daily:

"Last year, as each of you is aware, We decreed by an Encyclical Letter that, to win the help of Heaven for the Church in her trials, the great Mother of God should be honored by the means of the most holy Rosary during the whole of the month of October. In this We followed both Our own impulse and the example of Our predecessors, who in times of difficulty were wont to have recourse with increased fervor to the Blessed Virgin, and to seek her aid with special prayers. . .

. . . We therefore decree and make order that from the 1st of October to the 2nd of November following in all the parish churches, in all public churches dedicated to the Mother of God, or in such as are appointed by the Ordinary, five decades at least of the Rosary be recited, together with the Litany. If in the morning, the Holy Sacrifice will take place during these prayers; if in the evening, the Blessed Sacrament will be exposed for the adoration of the faithful; after which those present will receive the customary Benediction. We desire that, wherever it be lawful, the local confraternity of the Rosary should make a solemn procession through the streets as a public manifestation of religious devotion."
 

Text taken from here