Jones leaves the Turf for Hillsborough
The Owls activated a release clause in his contract, and Jones leaves Turf Moor for an undisclosed fee after three years, having signed on a free transfer after his release from Wigan Athletic.
Jones played an integral role in two promotion campaigns and has been promoted four times in all to the Premier League.
Burnley boss Sean Dyche said: “David has been fantastic over three-years at Burnley Football Club and given everything to the cause.
“He’s played a massive part in all we have achieved, and he’s activated a clause in his contract, which showed good will for a player who is 31.
“He has moved forward and we wish him well."
Jones made a total of 131 appearances for the Clarets, scoring three goals.