The Daughters of Charity Provincial Archives website explains:

June 3, 1905 marks the day that Pope Pius X formally recognized associations that had been formed for promoting the devotion popularly known as the Miraculous Medal… In order to spread devotion to Mary as our Lady of the Miraculous Medal, an association was formed shortly after the first medals were distributed. The Association was established at the motherhouse of the Congregation of the Mission in Paris. Gradually, other associations were established elsewhere in the world. Pope Pius X recognized these associations in 1905 and approved a charter in 1909.

Read more at the International Miraculous Medal Association.