The 30-year-old was released by relegated Chester at the end of last season despite being their top scorer with 18 goals and is excited at the prospect of playing for the Shakers.
Lowe said: "I am made up to be signing for Bury, I had offers from a few clubs, but I feel this club, under Alan Knill and Chris Brass, is going places.
"I saw Bury at close quarters in the two games I played against them last season, and I also watched them when they were very unlucky in the play-off semi-final against Shrewsbury. They have some very good players.
"Andy Bishop, Andy Morrell and Glynn Hurst all scored goals last season and that was because there are some excellent creative players in the team."