In the English-speaking world, this Christmas anthem owes much of its popularity to its regular inclusion in the service of Nine Lessons and Carols broadcast annually from the Chapel of King's College, Cambridge, and also to its inclusion in the first volume of the widely-used Carols for Choirs series of songbooks. Here is a particularly clear recording of a performance by the Choral Scholars of University College, Dublin.
The composition of the piece is attributed to the German composer Peter Cornelius (1824-1874), but close listening will reveal that there are actually two songs going on here, one sung by the soloist and the other in the background by the choir; this needs a little explanation.
Cornelius wrote Die Könige (The Kings) as part of his cycle of Christmas songs Weihnachtslieder, published in 1856. It was written for solo voice and piano, but while the vocal melody and words were his own, Cornelius based the piano accompaniment on an old Lutheran chorale, Wie schön leuchtet der Morgenstern (How lovely shines the morning star). This was published in 1599 by the German composer Philipp Nicolai, though some claim the melody is even older. Numerous English translations have been made for church hymnals, and the sturdy tune has been adapted by J.S. Bach and other composers for inclusion in their own works.
Getting back to Cornelius's Die Könige (sometimes also known as Drei Könige), there seems to be no evidence that Cornelius himself ever made a choral arrangement of his song. However, the obvious trick is to have the choir sing not just the tune but also the words of Philipp Nicolai's chorale as a background to Cornelius's vocal solo, and there are a few such arrangements. The best-known is that by Sir Ivor Atkins (1869-1953), who was for many years the organist and choirmaster at Worcester Cathedral. This, with an English translation of the words by H.N. Bate, is the arrangement used by the Choir of King's College, Cambridge, and published by their musical director David Willcocks in the Carols for Choirs book.
Ivor Atkins' choral arrangement also seems to be the most widely used by German choirs as a setting for the original German words, though often with a soprano rather than a baritone soloist, as in this performance by the Augsburger Vokalensemble. There are other choral arrangements, however, such as this one by Robert Sund, sung by the Chor Leoni Men's Choir. And the Capella Musica Seoul perform a very other-worldly version with a solo baritone backed by a chorus of sopranos and altos.
Lastly, a hybrid: Philipp Nicolai's chorale sung with H.N. Bate's English version of the words, by Hastings College Choir.