The 31-year-old ex-Wigan trainee spent four seasons with the Brewers, helping them reach the Championship, but spent last season on loan at Oxford.
He has also played at Morecambe, Accrington, Stevenage and Rochdale.
"Phil is very much like Jermaine Beckford in that he has been successful in gaining promotion out of this league," said boss Lee Clark.
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League One side Bury have signed right-back Phil Edwards on a two-year deal after his release by Burton.