It seems to be down to an ambiguous instruction issued by Pope Innocent III around 1200.
The Catholic Encyclopedia has this [extract]:
[In the eleventh century] the manner of making [the sign of the Cross] in the West seems to have been identical with that followed at present in the East, i.e. only three fingers were used, and the hand traveled from the right shoulder to the left. The point, it must be confessed, is not entirely clear ... Still, a rubric in a manuscript copy of the York Missal clearly requires the priest when signing himself with the paten to touch the left shoulder after the right.
This seems reasonable: up until the Great Schism in 1087, the entire Church was likely to have had a single custom which had built up over the previous seven hundred or more years. [The Use of York was celebrated in northern England until the Reformation in the sixteenth century].
Fr William Saunders appears to have done some research:
The earliest formalized way of making the sign of the cross appeared about the 400s, during the Monophysite heresy which denied the two natures in the divine person of Christ and thereby the unity of the Holy Trinity. The sign of the cross was made from forehead to chest, and then from right shoulder to left shoulder with the right hand.
The use of two fingers to make a large gesture was a reaction to the heresy. The shape of the fingers and the hand was further formalised to indicate the Trinity (details in the article).
An instruction of Pope Innocent III (1198–1216) evidences the traditional practice but also indicates a shift in the Latin Rite practice of the Catholic Church: "The sign of the cross is made with three fingers, because the signing is done together with the invocation of the Trinity ... This is how it is done: from above to below, and from the right to the left, because Christ descended from the heavens to the earth, and from the Jews (right) He passed to the Gentiles (left)." While noting the custom of making the cross from the right to the left shoulder was for both the western and eastern Churches, Pope Innocent continued, "Others, however, make the sign of the cross from the left to the right, because from misery (left) we must cross over to glory (right), just as Christ crossed over from death to life, and from Hades to Paradise. [Some priests] do it this way so that they and the people will be signing themselves in the same way. You can easily verify this — picture the priest facing the people for the blessing — when we make the sign of the cross over the people, it is from left to right...." Therefore, about this time, the faithful began to imitate the priest imparting the blessing, going from the left shoulder to the right shoulder with an open hand. Eventually, this practice became the custom for the Western Church.
Even here, a thirteenth-century pope is specifying that clergy make the sign of the cross from the right to the left, but in order that they move the same way as the people (rather like a gym aerobics instructor) they may instead cross from left to right. It would appear to be this ambiguous instruction which engendered the confusion, with some clergy going one way and some the other and the people copying them — either copying the direction of motion as they saw it, or copying the movement of the priest (that is, going in the opposite direction). Things got hopelessly confused and have settled down as left-to-right.
The decree of Innocent III would not have been recognised by the Eastern Church, and they have carried on just as they always did.