Both players will see out the rest of the season with their current clubs.
O'Flaherty, 22, has played three times on permit for Ospreys and scored a try after only three minutes of his regional debut, against Harlequins.
Salmon, 23, plays at lock and spent time with Chinnor and London Irish before joining Rotherham.
"Tom's got genuine pace, genuine footwork, and he's very combative - he's not the biggest of players but he's powerful," Chiefs head coach Rob Baxter told BBC Radio Devon.
"What we've seen of Toby is he's got the core fundamental things we look for in front-five forwards when we bring them to the club, and that has been pretty successful for us in the past."
Bridgend winger Tom O'Flaherty and Rotherham forward Toby Salmon will join Premiership club Exeter Chiefs at the end of the season on two-year deals.