The full-back has been one of Sunderland's longest-serving players, but he turned down the offer a new deal and is finalising a move to the Britannia Stadium.
Bardsley, who joined from Manchester United in 2008, ended a difficult season on a high by helping the Black Cats escape relegation.
Paolo Di Canio had frozen out the former Scotland international during his spell in charge, but he was recalled by the Italian's successor Gus Poyet and repaid his faith in the closing months.
The 28-year-old was a regular in the side as Sunderland mounted a late survival push, eventually finishing in 14th place, four points clear of the drop-zone.
Poyet was hoping to retain one of his experienced performers, but he is set to complete a switch to Mark Hughes' Potters.