The 31-year-old moved to Edgar Street, initially on loan, in the summer of 2005 from Chester City and helped United gain promotion from the Conference at the end of the 2005-06 campaign.
Last season Brown was a virtual ever-present as Graham Turner's men won automatic promotion to League One, but he has now opted to head to Gigg Lane.
His agent, Jesse Learoyd-Hill, told Sky Sports: "Wayne is very happy to sign for Bury. He had some great times at Hereford and he wishes them well.
"He is looking forward to the new season and hoping he can help Bury challenge for promotion."