Murray - a championship winning manager with AFC Fylde last season - has replaced Mark Beard at Priory Lane.
His first target will be survival, not promotion with the club sitting in the drop zone and find themselves six points adrift.
Murray - who captained Mansfield to the National League title ten years ago - begins life back in the dug-out at Torquay United this weekend.
Chairman Simon Leslie added: “It was really important that we found an appointment who could continue with our desire to support players who have been let down by football, and in Adam Murray I believe we have found the right candidate.
“He has a proven track record of winning as a player and as a manager, as well as the exceptional turnaround he’s overseen at Cheltenham Town in recent months.
“He is buying into our vision, and that made the decision a no-brainer for us. The group are naturally low on confidence, and I believe Adam will turn that around.”