According to historians Procopius and Cedrenus, the church was originally erected by Emperor Justinian in the last years of his reign (559-560) near a fountain of water from a holy well situated outside the walls of Theodosius II in correspondence of today's Gate of Silivri. During hunting the Emperor noticed a small chapel surrounded by many women. Asking the meaning of the building, he was told that this was the “source of the miracles”. He at once ordered that a magnificent church be built there, with the material remaining after the erection of the Hagia Sophia.

According to a later legend, the sanctuary was erected by Emperor Leo I the Thracian (r. 457–474) because of a miracle that occurred when he was still a soldier. Before entering the City, Leo met a blind man who asked him to give him water. A female voice ordered the future Emperor to wet the eyes of the blind man with water from a nearby swamp. The same voice added that she had chosen that very place to be worshiped and that he would one day receive the crown to the empire. Leo followed her order and at once the blind man recovered his eyesight. After his accession to the throne, the Emperor erected a magnificent church on this place. This legend is possibly a later invention of the monks of the sanctuary. It is possible that, before the Justinian's building was erected, a small monastery had already existed there.

Source: Wikipedia