Smith, who will join the Owls from Notts County in May, will work alongside current first-team physio Mark Palmer. Wednesday recently recruited full-time masseuse Derry Sutter from the English Institute of Sport and have invested heavily in new medical equipment.
Owls manager Brian Laws said: "Paul is another part of the jigsaw that we're putting together so that we have the resources and the experience to minimise the injuries that we have suffered over the last few years.
"The medical department has been depleted and stretched to its maximum and now, as the chairman has realised, we need to get the infrastructure right. We now have two top-quality physios supported by a part-time physio and a full-time masseur."
Owls chairman Lee Strafford added: "Adding Paul and Derry to the team sees us put in place the last piece of our sports medicine picture. From a sports medicine perspective we should now be well positioned to go into a full season set up as a strong Championship club."