&grabThe Wearing of the Green (and, indeed, at least one English Morris tune) is directly descended from the Scottish tune The Tulip, composed by James Oswald and first published in c.1747, if the experts are to be believed (I don't see why not). More information at Andrew Kuntz's The Fiddler's Companion:
The Tulip (search results)
In answer to your question in another thread, it would seem unlikely that there were any old Gaelic lyrics set to this tune, but there may well be modern ones.
Arrah Na Pogue was a stage show written by Dion Boucicault and E.H. House. You can see sheet music of 1865 for Boucicault's Wearing of the Green at the Lester Levy Sheet Music Collection:
Wearing of the Green.
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