Barry-Murphy has been seeking a new club since being released by The Owls at the end of last season.
The Irishman was a regular for Chris Turner during 18 months at Hillsborough but was axed as part of a squad overhaul.
He has now pitched up at Gigg Lane and has signed a one-year contract with the League Two outfit.
The 25-year-old returns to the North West with Bury after starting his English career with Preston North End in 1999.
