Other scholarship points to a Philadelphia insurance salesman:
SAY, BROTHER, WHO WROTE THIS MELODY?
Oh, goody. Battling links.
Both links claim unverified origins to the tune, but mine does cite a source where the original song was included in 1852, three years before the Philadelphia salesman claimed he wrote it. I've not been able to locate an 1852 version of the hymn book where it supposedly appeared, but it does not show up in later editions of that hymn book.
I gather that there were a number of claims of authorship. Here is another source that said it was originally a fundamentalist camp meeting song. Link. Certainly the "Glory, Glory, Hallelujah!" suggests a camp meeting origin.