In an article about the presence / absence of Gaelic in the movie, "Gaelic in Disney", in Celtic Life International, 2015, Dr Emily McEwen-Fujita quotes from the following about the song from an Atlantic Gaelic Academy e-newsletter:

“This song is thought to have originally been a Scottish pipe tune and the tune was used for an English song composed in the United States by Bernard Covert. One version of it, called, Jamie’s on the Stormy Sea, appeared in the journal of the whaling ship Euphrasia in 1849. The song crossed the Atlantic and was set to Gaelic words by Henry Whyte, who wrote under the pen-name Fionn. The Gaelic version came to Cape Breton in the St. Columba collection of Gaelic songs and used to be sung by Tommy MacDonald of the North Shore Singers. It was from Tommy’s singing that Julie Fowlis learned the song.”

Best,
Jim