Former Brentford boss Scott has signed a contract until the end of next season and will have Terry Bullivant as his assistant.
The pair previously spent more than three years together at Griffin Park, leading Brentford to the League Two title in 2009.
A repeat of that achievement will not happen this season - the run of seven points from as many games which cost Holdsworth his job has left Aldershot 20th in the table.
But a statement from the club made it clear Scott's appointment is with future success in mind.
It read: "The board of directors felt Andy and Terry offered the football club a real opportunity of making progress in the immediate and longer term."