The reference to Handel seems to have been a form of dedication.
The following is largely repetition of what Genie has posted, but it is put in a logical order by the editors of "Hymns and Carols of Christmas."

Original lyrics by Watts. Words Isaac Watts, based on Psalm 98, Part 2, "The Messiah's coming and kingdom."
Tume: Music" "Antioch," Lowell Mason, 1848.
Four stanzas as written by Watts. Another musical setting is by Nicolaus Hermann, 1485-1561, seldom heard.

Version most commonly sung, also four stanzas but differs from the version written by Watts.
Music by Lowell Mason, as noted above.
There are alternate tunes by P. C. Lutkin, Thomas Haweis and Henry Lahee (and possibly others).

Words by Watts, Music by Mason, but in arrangement by Joshua Sylvestre, "Christmas Carols- Ancient and Modern," c. 1861.

Watts and Mason, but arr. by William Henry Husk, "Songs of the Nativity," 1868. Three stanzas only, words quite different.

These two popular carol books, and others, have added to the confusion by not being clear or accurate in citations.

Scholars have not found the tune, or part of it, in any of the music composed by Handel.

All of these versions are reproduced in their entirety in "Hymns and Carols of Christmas." Start with the original Watts lyrics:
Joy 2

(Am I helping, or just adding to the confusion? I have an old Oxford Book of Carols, 1928 (1947); this carol is not included, although two others by Watts are given. Perhaps the editors threw up their hands.)