Walters, 33, has signed a two-year deal after spending seven years with the Potters, scoring 62 goals in 269 appearances.
He becomes Burnley's second summer signing after full-back Charlie Taylor joined from Championship side Leeds.
Walters' move means the Clarets now have five Republic of Ireland internationals in their squad.
He joins defenders Stephen Ward and Kevin Long, and midfielders Jeff Hendrick and Robbie Brady at Turf Moor.
Clarets striker Andre Gray, who has reportedly rejected a new contract, has been linked with a £15m move to fellow Premier League side West Ham.
Find all the latest football transfers on our dedicated page.
Burnley have signed Republic of Ireland striker Jon Walters from Stoke City for a fee that could reach £3m.