Lord I am not worthy

Someone recently asked me about the origin of the "Domine non sum dignus" prayer at Mass. Clearly it's based on the prayer of the centurion, "Domine, non sum dignus ut intres sub tectum meum : sed tantum dic verbo, et sanabitur puer meus." ("Lord, I am not worthy that thou shouldst enter under my roof: but only say the word, and my servant shall be healed." Matthew 8:8.) But when did it enter the liturgy?

Proclus of Constantinople (patriarch 434-446) preaches about this passage with a reference to our being unworthy for the Lord to enter "under the roof of our souls", but it does not become a liturgical prayer until much later. Amalarius of Metz (died c. 850) references this Gospel passage in reference to Communion, but seemingly without a connection to any established liturgical prayer. The writings of Pope Innocent III (De missarum mysteriis, PL 217.773 - 916, here 883) suggest that this prayer was still unknown in Rome in the early 13th century. In the north of France, however, Anselm of Laon (d. 1117) testified that the faithful said this prayer while approaching the Sacrament: “Domine non sum dignus, ut intres sub tectum meum." According to the two-volume edition of Jungmann's The Mass of the Roman Rite: its origins and development, the earliest known version of this prayer (much longer than the single sentence) is from the Sacramentary of Saint-Thierry, which dates to about 975 (vol. 2, pp. 355ff). So this is a late first-millenium gallican prayer. Lots of versions of this prayer exist in the West starting in France in the 10th century, but the final version we know today appears in a 12th or 13th century Sacramentary from lower Italy, and though it was lacking in the Missal of Trent, it was included in the Rituale Romanum of 1614.

I found a lot of good historical background on this question in "Non sum dignus/digna: pressing out the female voice" by Barry M. Craig.