The 39-year-old won two of his six games as player-manager of the Shakers after Lee Clark was sacked in October.
Nonetheless, Bury believe that Lowe is "the best candidate as he fits perfectly with the way the club wish to approach the future" and have handed the former centre-back a two-year deal.
"[Lowe] has a huge desire to create a successful side as manager and to replicate his playing experiences at Gigg Lane," the club said in a statement on their website.
"His affection for the club is there for everyone to see, and more than anything else, the board of directors feels he deserves a chance with his own players and style of play.
"Ryan is not afraid of giving young players a chance which is something that our supporters engage with, and the club openly encourages."
Lowe made 161 appearances in three spells with the club at centre-half, with his final appearance coming on March 30.