The 20-year-old re-joined Bury last week on loan, having enjoyed a productive spell (three goals in six substitute appearances) last term.
Rose signs for the Shakers for an undisclosed fee, and has penned a three-year deal at Gigg Lane.
With two goals in 18 appearances in his Reds career, Barnsley Football Club would like to wish Danny all the best in his future endeavours.
