Jepson was handed the caretaker reins last Monday following Kevin Blackwell's sacking, with the Shakers again battling at the wrong end of the table having been relegated from League One last term.
Ex-Gillingham boss Jepson, formerly Blackwell's assistant at Gigg Lane, lost 1-0 at Portsmouth in his opening fixture before guiding Bury to a goalless draw at home to Mansfield.
And, ahead of Saturday's trip to Wycombe, the club's board have seen enough to hand him the caretaker position on an extended basis.
A statement from the board on Bury's official website read: "The main priority at this time is to implement a state of stability that can support the players to regain the type of form that we know they are capable of.
"With this in mind and the fact that the players have demonstrated their full support for Ronnie Jepson, it has been decided to appoint Ronnie as the caretaker manager until January 2014. The current backroom team will also remain.
"This does allow the club to allow the dust to settle and assess the situation without being forced into any knee-jerk reactions."