The relic was discovered at the Manse Burn in Bearsden, East Dunbartonshire, after a young boy found fossils and showed them to a local expert.
A later excavation unearthed the one-metre-long Akmonistion zangerli.
Known as the Bearsden Shark, the "fossil wonder" is the only complete shark fossil of its kind in the world.
The plaque and cairn will be unveiled by Dr Neil Clark, curator of Palaeontology at Glasgow University's Hunterian Museum, where the fossil is now kept.
"The Bearsden Shark, the fossil wonder of the Hunterian's collections is the best-preserved fossil shark of its time in the world," he said.
"This was a very special discovery because in most fossils it is only the hard shelly, or bony, structures that are preserved while the soft tissues generally rot away.
"From the tip of its nose to the end of its tail, its fragile cartilage skeleton is almost intact after 330 million years locked in the black shales of Bearsden."
Dr Clarke added: "Even the partly digested remains of its last fish supper lie undisturbed still within the bowels of this one-metre-long fossil."
"Although the fossil has the scientific name Akmonistion zangerli, I am sure it will continue to be affectionately called the 'Bearsden Shark'."
The discovery is now being marked by a group of local residents who will display the plaque on a small cairn near the site.
East Dunbartonshire Council Provost Una Walker will help unveil both on Monday.
The provost said: "It is a source of great pride that such a significant scientific discovery was made in our area and it is thanks to the hard work of the local residents that the site is now properly marked."
A plaque and cairn will be unveiled later to mark the discovery of a unique 330-million-year-old fossilised shark that was found in Scotland in 1981.