They got that set from Nigel Gatherer's book Songs and Ballads of Dundee (Edinburgh: John Donald, 1985; the second edition, 2000, is still available), where it was printed "From the Poet's Box and the singing of Jim Reid". The Poet's Box being a prolific broadside publisher in Glasgow in the second half of the 19th century.

It seems that the final verse was added by Robert Burns for The Scots Musical Museum. The tune is fairly old, having first appeared in print in the 17th century.