Andy Stewart wrote this song, as he says in this video on YouTube. In the video he refers to it by the title A SCOTTISH SOLDIER and it appears that way on all the recordings carried by Spotify (and there are many; he seems to have recorded it more than once, and his recordings appear in many collections) but it appears on the sheet music as A SCOTTISH SOLDIER: GREEN HILLS OF TYROL, as can be seen in the catalog entries of several libraries here (I haven’t seen the actual sheet music; it is still under copyright and therefore not viewable online).

Interestingly, the songwriting credit from the sheet music says: “words by Andy Stewart ; arranged by Iain MacFadyen”; it doesn’t specifically identify the music. From this I infer that Stewart probably fitted his words to a traditional pipe tune, but I don’t recognize the tune.

There happens to be an entirely different song called GREEN HILLS OF TYROL with words by George Linley and music by G. Rossini, published “between 1827 and 1836.” You can see the sheet music at Internet Archive, and other places. This song seems to have nothing to do with Scotland. Tyrol is in Austria.

I have edited the above lyrics to add the songwriting credit, and have made some corrections to the text, so that it should now exactly agree with what Stewart sings.