Walters joins fellow Ireland players Jeff Hendrick, Stephen Ward, Robbie Brady and Kevin Long at Turf Moor after signing a two-year contract on Friday.
The 33-year-old, who has 49 caps for Ireland, scored 62 goals in 271 appearances in all competitions for Stoke during his seven years with the Potters.
Gutted to see @JonWalters19 leave. Gonna be a huge loss to the club and also the dressing room.— Charlie Adam (@Charlie26Adam) July 7, 2017
Walters is Burnley's second signing ahead of the new Premier League season, joining Charlie Taylor at the club after the left-back agreed a move from Leeds United.
The deals come after Burnley sold Michael Keane to Everton this week in a deal that could rise in value to £30m.