The tune is from Piae Cantiones (1582). The lyric if from Aurelius Clemens Prudentius (348 - c.410), a Romano-Spanish lawyer who composed religious poetry that was included into church offices in medieval times. The joining of the melody with the lyrics was the work of J. M. Neale in Carols for Christmastide (1853-54).
Some modern translations render the first line "Of the Father's love begotten" but "Of the Father's heart begotten" is more accurate.
I usually sing only the first four verses at Christmas Eve with handbell accompaniment.
It is included in The New Oxford Book of Carols (#19).