'Skye Boat Song' appeared in Songs of the North volume I, [1884 or 1885]. The editors were A C MacLeod (that is, Anne Campbell MacLeod) and Harold Boulton; the music was arranged by Malcolm Lawson.

There is some suggestion that the tune was ascribed in some fashion to Miss MacLeod in the first edition, but it was merely described in later editions (my copy is the 23rd edition; it was a very popular book) as an "old Highland rowing measure" (a 'iorram': describing it as a shanty is potentially misleading, though even the Oxford Companion to Music does so), but at any rate it is a matter of record that Anne MacLeod (later Lady Wilson) "heard the first part ... in 1879 while being rowed from Torrin to Loch Coruisk, in Skye. She added the second part herself and in 1884 Sir Harold Boulton ... wrote the words which have so captured the popular imagination." (Wilma Patterson, Songs of Scotland. Edinburgh: Mainstream Publishing, 1996, p 53).

It was common practice in 19th century Scotland to add a "second strain" to short tunes got from tradition. Naturally, the tune in its new form would be A C MacLeod's copyright, and, given the enormous number of times it has been reprinted and recorded, it isn't surprising that the copyright information has led some to assume that she wrote the whole thing.

In 1887, Stevenson heard a Miss Ferrier (granddaughter of Professor Wilson, who, under the pen name 'Christopher North' was himself quite a prolific provider of new words for old melodies) sing the song. He was keen on the tune but not much taken by the words, so he wrote some of his own. These were not published until after his death.

It is sometimes asserted that the unknown "rowing measure" was actually 'Cuachag nan Craobh', and there is certainly a superficial resemblance between the melodies. Andrew Kuntz ( Fiddlers Companion: Skye Boat Song ) paraphrases an anecdote that would seem to confirm the connection if it is authentic: unfortunately he cites no source, so it would be difficult to verify. Meanwhile, I'd treat the identification with caution.

See, in the DT:

SKYE BOAT SONG  (Boulton's text, missing the final verse)

OVER THE SEA TO SKYE (VARIANT)  (Robert Louis Stevenson text)

Among several past discussions, see:

Skye Boat Song  -includes RLS text, the Boulton verse missing from DT, and various other comments including a couple of parodies.