The left-back, 35, who has made over 500 appearances in the Football League, becomes the first signing under Bury's new ownership.
Roberts was on the books of Liverpool in his youth, winning the FA Youth Cup in 1996, before moving to Greece for a short spell at Panionios, where Liverpool legend Ronnie Whelan was manager.
His time in Greece was short-lived, however, and he returned to England to join Tranmere and played over 300 times for the Wirral club before moving to Doncaster and then Derby.
He won nine caps for Wales between 2000 and 2005.
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- the Football League