According to The Hymnal 1940 Companion, Church Pension Fund, New York, 1949, p. 3, "Th[e] metrical form firt appeard in the appendix to Psalterium Cantionum Catholicarum,, Cologne, 1710."
According to the same source, the melody, "Veni Emmanuel... appears to be a cento of several Kyrie melodies made by Thomas Helmore to accompany [John Mason] Neale's text in the musical edition of the Hymnal Noted, 1854. In that work he states that it is from a French Missal in te National Library at Lisbon, Portugal, but no identical melody has been found there."
This source is over 50 years old now, so maybe some earlier witnesses to the melody and to the metrical version of the text have been discovered since it was published. This same edition of the Hymnal Companion failed to identify the Bunting collection as the source of the melody Deirdre (though later editions did make this identification) so it is certainly not an infallible source.