Jepson, who played for the Shakers between 1996 and 1998, becomes right-hand man to Kevin Blackwell at Gigg Lane just hours after Shirtliff stepped down having expressed a desire to depart.
Jepson will start his new position with immediate effect as Bury, relegated to League Two, begin the job of rebuilding under new chairman Stewart Day, who only completed a takeover of the financially-stricken outfit at the end of last month.
"It's good to be back, I have some great memories of this place and a lot of success here," Jepson told the club's official website.
"When the gaffer rang me and offered me the job I didn't think twice. We had a quick chat and everything was sorted out quickly and I'm ready to go.
"I know where this club can go and I know Kevin Blackwell is very excited with the new ownership. In terms of the philosophy and where we are going to go, I am now a part of that and really looking forward to it.
"I've met the chairman and the team behind him. This is exciting times for this football club. It's a fresh start with new owners, plus I know Kevin from old. He wants to be successful and he's a driven man, the same as me."
Jepson has previous management experience at Gillingham while he has also held assistant and coaching roles with the likes of Burnley, Huddersfield, Crystal Palace, QPR and Leeds.