The duo arrived in Hampshire earlier this year and despite administration and relegation from the Football League at the end of last season, Aldershot are already off the bottom of the Conference after starting with a 10-point deduction.
Chairman Shahid Azeem said: "The board of directors are thrilled that both Andy and Terry have signed these three-year contracts. We were very keen to keep them both for the long-term, we enjoy working with them and know that we can trust them."
Scott added: "I can manage better when I've got Terry next to me. We get on very well and we understand each other.
"It's very encouraging that somebody who has worked with some very good managers wants to work with me. He's a real rock and somebody that I can lean on. All staff at the club are fantastic and I really enjoy working with them."
After 15 games of the Conference season, Aldershot are already within three points of escaping the drop zone.