Oley Speaks wrote a version, published in 1907.

Bellamy said in an interview: "We know that [Kipling] had specific tunes in mind when he wrote [the poems] but he never let on what they were." This could be an exception, of course.

There's a reference here to it having been written to a popular waltze tune.

Kipling himslef referred to it as a 'song' - though that was some time after it had become a song, I think.