Both men have joined Stoke, with Davies signing on a free transfer following the expiry of his Reds contract while Lindsay has been sold for an initial fee of £2million.
Following Ryan Hedges' decision to join Aberdeen, it means that three key players from the club's League One promotion season will not be around in the Championship.
Davies' exit has been no secret, though it will still hurt given his performances last season, where he kept a club-record number of clean sheets.
His displays over the last four years mean he will be remembered fondly at Oakwell.
Both men turned down new deals this summer, with Lindsay having a year to run on his existing contract.
The club have managed to get Jacob Brown, Cameron McGeehan and Cauley Woodrow tied down to long-term deals, but after Lindsay expressed his desire to move, a sale to Stoke was agreed.
Chief executive Paul Conway said: “We have offered 10 new contracts to players and coaching staff this summer.
“We are really pleased to see Jacob Brown, Cauley Woodrow, Mike Bähre and Cameron McGeehan sign new deals and there are plenty of ongoing discussions with others.
“Liam was one of the players we have offered a new contract to. After a hard-fought battle to keep Liam, we have reluctantly agreed to allow a transfer.”
A statement from the club added: “Barnsley Football Club thank Adam for his fantastic service over five years at the club and wish him well at Stoke City.”