From Boyd B. Stutler, Glory, Glory, Hallelujah!: The Story of "John Brown's Body" and "Battle Hymn of the Republic" (Printed and Bound by The C.J. Krehbiel Company, Cincinnati, [1960], pp. 40-47):

The origin of the air to which "John Brown's Body" and the "Battle Hymn" are adapted is lost in the midst of years....
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It was in the 1880's when "John Brown's Body"and its melody seemed to be fatherless things that claims and counter-claims to its composition were made by hopefuls who sought a place in the sun. Most perssistent in urging their claims were William Steffe, of Philadelphia, Thomas Brigham Bishop, of New York, and Frank E. Jerome, of Russell, Kansas--but each case their claims can easily be dismissed on examination of the records and proven facts....
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The William Steffe myth, ..., is the one that has really muddied the waters, and he is the one who has profited most--in name only--from his assertion that he composed the music of "John Brown's Body," later to be almost completely captured by "The Battle Hymn of the Republic." In fact his name as composer heads the music in many of the song books current today.
Whatever his private claims may have been, Steffe was not publicly credited with the composition until November 3, 1883, when Major O.C. Bosbyshell published an article entitled "Origin of 'John Brown's Body'" in Grand Army Scout and Soldiers' Mail, of Philadelphia. The piece was picked up by Brander Matthews for use in his "Songs of the War," in Century Magazine, August, 1887, thus putting Steffe on the road to fame. He died at his Philadelphia home on May 5, 1911.
Steffe's claim is fully set out in a series of letters written to Colonel Richard J. Hinton running from 1885 to 1887, now lodged in the Kansas Historical Society library. His story is that in 1855 or 1856 he was asked to write an air for a series of verses beginning "Say, bummers, will you meet us?" which the Good Will Engine Company, of Philadelphia, wanted to sing to welcome the Liberty Fire Company, of Baltimore, then due to pay a fraternal visit to the firemen of the Quaker City. It was the Bosbyshell claim that the air composed, set to the "Say, bummers, will you meet us?" verse, had such snap and verse that it was immediately caught up by revivalists, substituting "Say, brothers, will you meet us?" for the first verse, then carried throughout the country. But the tune was an old one when Steffe's grandfather was young; what he probably did was to pick up the old air, maybe from a sub-conscious memory, and revamp it to fit the firemen's welcoming song.
Steffe was a life-long Philadelphian. His activities can be traced through the years as a clerk, insurance agent, manager of a heating stove works, and as an active Mason for more than fifty years--but in all the record there is no mention of him as a composer of music other than the John Brown tune. In some way most of the narrators, Major Bosbyshell excluded, have transported him to the South, usually represented as a Charleston, South Carolina, music writer, but sometimes from Richmond, Virgina--and the statement is frequently made that a Northerner (Daniel Decatur Emmet) wrote "Dixie," the great war song of the South, and a Southerner (William Steffe?) wrote the most popular war son of the North, "John Brown's Body."
Anyway, Steffe has reaped a rich reward of unearned posthumous fame.