The song seems to have originated from the Gene Autry film series "Phantom Empire," and sheet music printed in 1935 credits Autry and Smiley Burnette as songwriters. It wouldn't be the first time a trad. song has been claimed by others, though. With archive.org down for the moment, I can't investigate further, but I didn't find any examples on newspapers.com predating 1936 (as part of an American Legion Minstrel show; see Express and Standard [Newport, VT] Jan 17, 1936, p. 1). Note that it is not included in the 1933 Silly Symphony film "Father Noah's Ark," which was advertized in some period literature as "Uncle Noah's Ark."

Listen to an interpretation of the 1935 sheet music here. Lyrics not substantively different from either of the above, or see Autry's performance of it here; they performed it again in Round-Up Time in Texas.