The 29-year-old, who found the net a total of 69 times during a four-year spell with the Valiants, had been a free agent after leaving Vale Park at the end of last season.
"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," manager David Flitcroft told Bury's official website.
"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."
Pope scored 12 goals for Port Vale during the 2014-15 campaign.