The Tannahill's set varies in a few words from that in the DT as Jimmy Raeburn, and lacks a verse. They don't credit any source for the version they recorded, but traditional versions don't vary all that much anyway. Ewan MacColl (Travellers' Songs from England and Scotland (1977) commented:

"In a note written for The Buchan Observer of August 1908, [Gavin] Greig described this transportation ballad as being one of the most popular folksongs we have. Seven years earlier, [Robert] Ford had written that it was long a popular song all over Scotland, and sold readily in penny-sheet forms. [Frank] Kidson knew it from several broadsides under the title of The Hills of Caledonia Oh.

The hero of the song was, according to Ford, a baker to trade who was sentenced to banishment for theft more than sixty years before. Commenting on this, Greig refers to search of the Glasgow criminal records by John Ord, who failed to find any person of the name of James Raeburn who had been banished from Glasgow for theft or any other crime during that period." This period would presumably be around the 1830s.

There are several broadside copies at Bodleian Library Broadside Ballads:

James Raeburn  Printer and date unknown.

James Raeburn  Printer and date unknown.

Jamie Raeburn  Printed between 1851 and 1910 by Lindsay, J.? (Glasgow?)

Jamie Raeburn  Printed by The Poet's Box (Glasgow); date missing, but these are usually 1850-1880.

Willie Scott's tune (unlikely to be very different from the Tannahill arrangement) can be found at The Mudcat Midi Pages:

Jamie Raeburn.mid