The 32-year-old has put pen to paper on a two-year contract and becomes the fourth new arrival for the Clarets this summer, following former Stoke team-mate Jonathan Walters to Turf Moor.
The moves means a return to the club where Bardsley spent a month on loan in the Championship in 2006.
He told Clarets Player HD: "I've had different spells and different clubs since then and I'm delighted to be back.
"It's a club that's going in the right direction with a fantastic manager and a great group of players which I'm looking forward to being part of.