Verses 1 & 2, were written by an anonymous author, Some sources show the author as Martin Luther; this attribution (probably incorrect) is based on the title 'Luther's Cradle Hymn,' given to these words by the composer, James Murray. Verse 3 is by John Thomas McFarland (1851-1913).
Thanks to Richard W. Adams for doing this research.
'Mueller,' James R. Murray, 1887
Lyrics and chords available from Folk Den Project.