The 29-year-old’s contract at Port Vale expired at the end of the season and he was in demand.
Bury boss David Flitcroft was delighted to get his man and told the club’s official website: “As Tom’s record shows he is a proven goalscorer and he made a massive contribution to Port Vale during his time at the club.
“He is a renowned goalscorer who can score all different types of goals. With the level of striker that we already have at the Club I am looking forward to whichever strike combination we choose.
“He is the ultimate team player who values team work above everything else. He has an incredible work ethic, industry and enthusiasm to his game. His enthusiasm will drive us as a club and players around him.
“I believe that he is a player that the fans will soon take into their hearts.”
Pope was a prolific goalscorer at Vale Park, netting 69 times since moving from Rotherham in 2011.